A new type of coupled Korteweg de-Vries equation is found to be Painlevé-integrable. The new model is a special case which can be used to describe two-layer fluids with different dispersion relations.
In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several ki...In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several kinds of exact（new） solutions of the generalized KdV equation are obtained.展开更多
This article describes some dynamic aspects on dynastic utility incorporating two-sided altruism with an OLG setting. The special case is analyzed where the weights of two-sided altruism are dynamically inconsistent. ...This article describes some dynamic aspects on dynastic utility incorporating two-sided altruism with an OLG setting. The special case is analyzed where the weights of two-sided altruism are dynamically inconsistent. The Bellman equation for two-sided altruism proves to be reduced to one-sided dynamic problem, but the effective discount factor is different only in the current generation. It is shown that a contraction mapping result of value function cannot be achieved in general, and that there can locally exist an infinite number of self-consistent policy functions of the class C＂ with distinct steady states （indeterminacy of self-consistent, differentiable policy functions）.展开更多
This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectio...This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectional propagation of long-wave in dispersive media and GSEs are used to model the interaction between one-dimensional high,and low-frequency waves.Classes of trigonometric and hyperbolic function solutions in fractional calculus are discussed.Graphical simulations of the numerical solutions are flaunted by MATLAB.展开更多
Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other m...Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.展开更多
In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation e...In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.展开更多
In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogene...In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many others.Building on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal operators.Due to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest.展开更多
In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the ...In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the cubic form.The main ingredient here is the establishment of the L^(2)-L^(∞)decay estimates and the energy estimates for the linear problem,which are adapted to the wave equation on the product space.The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction,the scaling technique,and the combination of the decay estimates and the energy estimates.展开更多
Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained thro...Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained through the Hirota method and symbolic computation. Breather-like and bound-state solitons are constructed in which the signs of the imaginary parts of the complex wave numbers and the initial separations of the two parallel solitons are important factors for the interaction patterns. The periodic structures and position-induced phase shift of some solutions are introduced.展开更多
Based on an algebraically Rossby solitary waves evolution model,namely an extended(2+1)-dimensional Boussinesq equation,we firstly introduced a special transformation and utilized the Hirota method,which enable us to ...Based on an algebraically Rossby solitary waves evolution model,namely an extended(2+1)-dimensional Boussinesq equation,we firstly introduced a special transformation and utilized the Hirota method,which enable us to obtain multi-complexiton solutions and explore the interaction among the solutions.These wave functions are then employed to infer the influence of background flow on the propagation of Rossby waves,as well as the characteristics of propagation in multi-wave running processes.Additionally,we generated stereogram drawings and projection figures to visually represent these solutions.The dynamical behavior of these solutions is thoroughly examined through analytical and graphical analyses.Furthermore,we investigated the influence of the generalized beta effect and the Coriolis parameter on the evolution of Rossby waves.展开更多
Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are provided.Based...Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are provided.Based on these bilinear equations, some exact solutions to the three modified equations are derived.展开更多
In the generalized continuum mechanics(GCM)theory framework,asymmetric wave equations encompass the characteristic scale parameters of the medium,accounting for microstructure interactions.This study integrates two th...In the generalized continuum mechanics(GCM)theory framework,asymmetric wave equations encompass the characteristic scale parameters of the medium,accounting for microstructure interactions.This study integrates two theoretical branches of the GCM,the modified couple stress theory(M-CST)and the one-parameter second-strain-gradient theory,to form a novel asymmetric wave equation in a unified framework.Numerical modeling of the asymmetric wave equation in a unified framework accurately describes subsurface structures with vital implications for subsequent seismic wave inversion and imaging endeavors.However,employing finite-difference(FD)methods for numerical modeling may introduce numerical dispersion,adversely affecting the accuracy of numerical modeling.The design of an optimal FD operator is crucial for enhancing the accuracy of numerical modeling and emphasizing the scale effects.Therefore,this study devises a hybrid scheme called the dung beetle optimization(DBO)algorithm with a simulated annealing(SA)algorithm,denoted as the SA-based hybrid DBO(SDBO)algorithm.An FD operator optimization method under the SDBO algorithm was developed and applied to the numerical modeling of asymmetric wave equations in a unified framework.Integrating the DBO and SA algorithms mitigates the risk of convergence to a local extreme.The numerical dispersion outcomes underscore that the proposed SDBO algorithm yields FD operators with precision errors constrained to 0.5‱while encompassing a broader spectrum coverage.This result confirms the efficacy of the SDBO algorithm.Ultimately,the numerical modeling results demonstrate that the new FD method based on the SDBO algorithm effectively suppresses numerical dispersion and enhances the accuracy of elastic wave numerical modeling,thereby accentuating scale effects.This result is significant for extracting wavefield perturbations induced by complex microstructures in the medium and the analysis of scale effects.展开更多
Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which d...Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which depicts the shear properties of concrete.The experiments on the EoS of concrete is always challenging due to the technical difficulties and equipment limitations,especially for the specimen size effect on the EoS.Although some researchers investigate the shock properties of concretes by fly-plate impact tests,the specimens used in their tests are usually in one size.In this paper,the fly-plate impact tests on concrete specimens with different sizes are performed to investigate the size effect on the shock properties of concrete materials.The mechanical background of the size effect on the shock properties are revealed,which is related to the lateral rarefaction effect and the deviatoric stress produced in the specimen.According to the tests results,the modified EoS considering the size effect on the shock properties of concrete are proposed,which the bulk modulus of concrete is unpredicted by up to 20% if size effects are not accounted for.展开更多
In this article,we consider the diffusion equation with multi-term time-fractional derivatives.We first derive,by a subordination principle for the solution,that the solution is positive when the initial value is non-...In this article,we consider the diffusion equation with multi-term time-fractional derivatives.We first derive,by a subordination principle for the solution,that the solution is positive when the initial value is non-negative.As an application,we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a subdomain.Finally,several numerical experiments are presented to show the accuracy and efficiency of the algorithm.展开更多
This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽...This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.展开更多
In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic sol...In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications.展开更多
The evolution of the probability density function of a stochastic dynamical system over time can be described by a Fokker–Planck–Kolmogorov(FPK) equation, the solution of which determines the distribution of macrosc...The evolution of the probability density function of a stochastic dynamical system over time can be described by a Fokker–Planck–Kolmogorov(FPK) equation, the solution of which determines the distribution of macroscopic variables in the stochastic dynamic system. Traditional methods for solving these equations often struggle with computational efficiency and scalability, particularly in high-dimensional contexts. To address these challenges, this paper proposes a novel deep learning method based on prior knowledge with dual training to solve the stationary FPK equations. Initially, the neural network is pre-trained through the prior knowledge obtained by Monte Carlo simulation(MCS). Subsequently, the second training phase incorporates the FPK differential operator into the loss function, while a supervisory term consisting of local maximum points is specifically included to mitigate the generation of zero solutions. This dual-training strategy not only expedites convergence but also enhances computational efficiency, making the method well-suited for high-dimensional systems. Numerical examples, including two different two-dimensional(2D), six-dimensional(6D), and eight-dimensional(8D) systems, are conducted to assess the efficacy of the proposed method. The results demonstrate robust performance in terms of both computational speed and accuracy for solving FPK equations in the first three systems. While the method is also applicable to high-dimensional systems, such as 8D, it should be noted that computational efficiency may be marginally compromised due to data volume constraints.展开更多
This paper is devoted to the Cauchy problem for the generalized damped Boussinesq equation with a nonlinear source term in the natural energy space.With the help of linear time-space estimates,we establish the local e...This paper is devoted to the Cauchy problem for the generalized damped Boussinesq equation with a nonlinear source term in the natural energy space.With the help of linear time-space estimates,we establish the local existence and uniqueness of solutions by means of the contraction mapping principle.The global existence and blow-up of the solutions at both subcritical and critical initial energy levels are obtained.Moreover,we construct the sufficient conditions of finite time blow-up of the solutions with arbitrary positive initial energy.展开更多
This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the ...This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers.By analyzing the Lax pair and the Riemann–Hilbert problem,we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system.Furthermore,we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors.Through appropriate parameter selections,we observe various nonlinear phenomena,including the disappearance of solitons after interaction and their transformation into breather-like solitons,as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.展开更多
The Landau equation is studied for hard potential with-2≤γ≤1.Under a perturbation setting,a unique global solution of the Cauchy problem to the Landau equation is established in a critical Sobolev space H_(x)^(d)L_...The Landau equation is studied for hard potential with-2≤γ≤1.Under a perturbation setting,a unique global solution of the Cauchy problem to the Landau equation is established in a critical Sobolev space H_(x)^(d)L_(v)^(2)(d>3/2),which extends the results of[11]in the torus domain to the whole space R_(x)^(3).Here we utilize the pseudo-differential calculus to derive our desired result.展开更多
基金The project supported by National Natural Science Foundation of China under Grant Nos. 90203001, 10475055, 90503006, and 10547124The authors are indebted to Dr. F. Huang and Prof. Y. Chen for their helpful discussions.
文摘A new type of coupled Korteweg de-Vries equation is found to be Painlevé-integrable. The new model is a special case which can be used to describe two-layer fluids with different dispersion relations.
基金Foundation item： Supported by the National Natural Science Foundation of China（10671182） Supported by the Foundation and Frontier Technology Research of Henan（082300410060）
文摘In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several kinds of exact（new） solutions of the generalized KdV equation are obtained.
文摘This article describes some dynamic aspects on dynastic utility incorporating two-sided altruism with an OLG setting. The special case is analyzed where the weights of two-sided altruism are dynamically inconsistent. The Bellman equation for two-sided altruism proves to be reduced to one-sided dynamic problem, but the effective discount factor is different only in the current generation. It is shown that a contraction mapping result of value function cannot be achieved in general, and that there can locally exist an infinite number of self-consistent policy functions of the class C＂ with distinct steady states （indeterminacy of self-consistent, differentiable policy functions）.
文摘This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectional propagation of long-wave in dispersive media and GSEs are used to model the interaction between one-dimensional high,and low-frequency waves.Classes of trigonometric and hyperbolic function solutions in fractional calculus are discussed.Graphical simulations of the numerical solutions are flaunted by MATLAB.
文摘Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.
基金supported by the NSFC(12101012)the PhD Scientific Research Start-up Foundation of Anhui Normal University.Zeng’s research was supported by the NSFC(11961160716,11871054,12131017).
文摘In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.
基金supported by Ministry of Education and Training(Vietnam),under grant number B2023-SPS-01。
文摘In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many others.Building on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal operators.Due to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest.
文摘In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the cubic form.The main ingredient here is the establishment of the L^(2)-L^(∞)decay estimates and the energy estimates for the linear problem,which are adapted to the wave equation on the product space.The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction,the scaling technique,and the combination of the decay estimates and the energy estimates.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12161061)the Fundamental Research Funds for the Inner Mongolia University of Finance and Economics (Grant No. NCYWT23036)+2 种基金the Young Innovative and Entrepreneurial Talents of the Inner Mongolia Grassland Talents Project in 2022,Autonomous Region “Five Major Tasks” Research Special Project for the Inner Mongolia University of Finance and Economics in 2024 (Grant No. NCXWD2422)High Quality Research Achievement Cultivation Fund for the Inner Mongolia University of Finance and Economics in 2024 (Grant No. GZCG2426)the Talent Development Fund of Inner Mongolia Autonomous Region, China。
文摘Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained through the Hirota method and symbolic computation. Breather-like and bound-state solitons are constructed in which the signs of the imaginary parts of the complex wave numbers and the initial separations of the two parallel solitons are important factors for the interaction patterns. The periodic structures and position-induced phase shift of some solutions are introduced.
基金Supported by the National Natural Science Foundation of China(No.32360249)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(No.2022QN01003)+2 种基金the University Scientific Research Project of Inner Mongolia Autonomous Region of China(No.NJZY22484)the Scientific Research Improvement Project of Youth Teachers of Inner Mongolia Autonomous Region of China(No.BR230161)the Inner Mongolia Agricultural University Basic Discipline Scientific Research Launch Fund(No.JC2020003)。
文摘Based on an algebraically Rossby solitary waves evolution model,namely an extended(2+1)-dimensional Boussinesq equation,we firstly introduced a special transformation and utilized the Hirota method,which enable us to obtain multi-complexiton solutions and explore the interaction among the solutions.These wave functions are then employed to infer the influence of background flow on the propagation of Rossby waves,as well as the characteristics of propagation in multi-wave running processes.Additionally,we generated stereogram drawings and projection figures to visually represent these solutions.The dynamical behavior of these solutions is thoroughly examined through analytical and graphical analyses.Furthermore,we investigated the influence of the generalized beta effect and the Coriolis parameter on the evolution of Rossby waves.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11931017 and 12071447)。
文摘Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are provided.Based on these bilinear equations, some exact solutions to the three modified equations are derived.
基金supported by project XJZ2023050044,A2309002 and XJZ2023070052.
文摘In the generalized continuum mechanics(GCM)theory framework,asymmetric wave equations encompass the characteristic scale parameters of the medium,accounting for microstructure interactions.This study integrates two theoretical branches of the GCM,the modified couple stress theory(M-CST)and the one-parameter second-strain-gradient theory,to form a novel asymmetric wave equation in a unified framework.Numerical modeling of the asymmetric wave equation in a unified framework accurately describes subsurface structures with vital implications for subsequent seismic wave inversion and imaging endeavors.However,employing finite-difference(FD)methods for numerical modeling may introduce numerical dispersion,adversely affecting the accuracy of numerical modeling.The design of an optimal FD operator is crucial for enhancing the accuracy of numerical modeling and emphasizing the scale effects.Therefore,this study devises a hybrid scheme called the dung beetle optimization(DBO)algorithm with a simulated annealing(SA)algorithm,denoted as the SA-based hybrid DBO(SDBO)algorithm.An FD operator optimization method under the SDBO algorithm was developed and applied to the numerical modeling of asymmetric wave equations in a unified framework.Integrating the DBO and SA algorithms mitigates the risk of convergence to a local extreme.The numerical dispersion outcomes underscore that the proposed SDBO algorithm yields FD operators with precision errors constrained to 0.5‱while encompassing a broader spectrum coverage.This result confirms the efficacy of the SDBO algorithm.Ultimately,the numerical modeling results demonstrate that the new FD method based on the SDBO algorithm effectively suppresses numerical dispersion and enhances the accuracy of elastic wave numerical modeling,thereby accentuating scale effects.This result is significant for extracting wavefield perturbations induced by complex microstructures in the medium and the analysis of scale effects.
基金supported by the National Natural Science Foundation of China[Grant Nos.51938011 and 51908405]Australian Research Council。
文摘Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which depicts the shear properties of concrete.The experiments on the EoS of concrete is always challenging due to the technical difficulties and equipment limitations,especially for the specimen size effect on the EoS.Although some researchers investigate the shock properties of concretes by fly-plate impact tests,the specimens used in their tests are usually in one size.In this paper,the fly-plate impact tests on concrete specimens with different sizes are performed to investigate the size effect on the shock properties of concrete materials.The mechanical background of the size effect on the shock properties are revealed,which is related to the lateral rarefaction effect and the deviatoric stress produced in the specimen.According to the tests results,the modified EoS considering the size effect on the shock properties of concrete are proposed,which the bulk modulus of concrete is unpredicted by up to 20% if size effects are not accounted for.
基金supported by National Natural Science Foundation of China(12271277)the Open Research Fund of Key Laboratory of Nonlinear Analysis&Applications(Central China Normal University),Ministry of Education,China.
文摘In this article,we consider the diffusion equation with multi-term time-fractional derivatives.We first derive,by a subordination principle for the solution,that the solution is positive when the initial value is non-negative.As an application,we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a subdomain.Finally,several numerical experiments are presented to show the accuracy and efficiency of the algorithm.
基金supported by the National Natural Science Foundation of China(12271296,12271195).
文摘This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.
文摘In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications.
基金Project supported by the National Natural Science Foundation of China (Grant No.12172226)。
文摘The evolution of the probability density function of a stochastic dynamical system over time can be described by a Fokker–Planck–Kolmogorov(FPK) equation, the solution of which determines the distribution of macroscopic variables in the stochastic dynamic system. Traditional methods for solving these equations often struggle with computational efficiency and scalability, particularly in high-dimensional contexts. To address these challenges, this paper proposes a novel deep learning method based on prior knowledge with dual training to solve the stationary FPK equations. Initially, the neural network is pre-trained through the prior knowledge obtained by Monte Carlo simulation(MCS). Subsequently, the second training phase incorporates the FPK differential operator into the loss function, while a supervisory term consisting of local maximum points is specifically included to mitigate the generation of zero solutions. This dual-training strategy not only expedites convergence but also enhances computational efficiency, making the method well-suited for high-dimensional systems. Numerical examples, including two different two-dimensional(2D), six-dimensional(6D), and eight-dimensional(8D) systems, are conducted to assess the efficacy of the proposed method. The results demonstrate robust performance in terms of both computational speed and accuracy for solving FPK equations in the first three systems. While the method is also applicable to high-dimensional systems, such as 8D, it should be noted that computational efficiency may be marginally compromised due to data volume constraints.
基金supported by the National Natural Science Foundation of China(12301272)the Natural Science Foundation of Henan(202300410109)the Cultivation Programme for Young Backbone Teachers in Henan University of Technology,and the Innovative Funds Plan of Henan University of Technology(2020ZKCJ09).
文摘This paper is devoted to the Cauchy problem for the generalized damped Boussinesq equation with a nonlinear source term in the natural energy space.With the help of linear time-space estimates,we establish the local existence and uniqueness of solutions by means of the contraction mapping principle.The global existence and blow-up of the solutions at both subcritical and critical initial energy levels are obtained.Moreover,we construct the sufficient conditions of finite time blow-up of the solutions with arbitrary positive initial energy.
基金supported by the Natural Science Foundation of Hebei Province,China (Grant No.A2021502004)the Fundamental Research Funds for the Central Universities (Grant No.2024MS126).
文摘This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers.By analyzing the Lax pair and the Riemann–Hilbert problem,we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system.Furthermore,we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors.Through appropriate parameter selections,we observe various nonlinear phenomena,including the disappearance of solitons after interaction and their transformation into breather-like solitons,as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.
文摘The Landau equation is studied for hard potential with-2≤γ≤1.Under a perturbation setting,a unique global solution of the Cauchy problem to the Landau equation is established in a critical Sobolev space H_(x)^(d)L_(v)^(2)(d>3/2),which extends the results of[11]in the torus domain to the whole space R_(x)^(3).Here we utilize the pseudo-differential calculus to derive our desired result.
