In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with ...In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.展开更多
The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier c...The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf- ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.展开更多
The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper...The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.展开更多
This paper investigates the asymptotic behavior of end effects for a Stokes flow defined on a three-dimensional semi-infinite cylinder. With homogeneous Dirichlet conditions of the velocity on the lateral surface of t...This paper investigates the asymptotic behavior of end effects for a Stokes flow defined on a three-dimensional semi-infinite cylinder. With homogeneous Dirichlet conditions of the velocity on the lateral surface of the cylinder, solutions either grow or decay exponentially in the distance from the finite end of the cylinder. In the case of decay, the effect of perturbing the equation parameters is also investigated.展开更多
The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results a...The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations.展开更多
Reference [1] deals with the uniqueness of solution to problem （A） and solution of problem （A） is continuously dependent on free term and initial value under certain conditions. This paper discuss the solution of ...Reference [1] deals with the uniqueness of solution to problem （A） and solution of problem （A） is continuously dependent on free term and initial value under certain conditions. This paper discuss the solution of problem （A） is continuously dependent on boundary value on the basis of references [2] and [3].展开更多
The structural stability for the Brinkman-Forchheimer equations with temperature-dependent solubility in a bounded region in R3 was studied.The reaction boundary conditions for the temperature T and the salt concentra...The structural stability for the Brinkman-Forchheimer equations with temperature-dependent solubility in a bounded region in R3 was studied.The reaction boundary conditions for the temperature T and the salt concentration were imposed.With the aid of some useful a priori bounds,we were able to demonstrate the continuous dependence result for the Forchheimer coefficient λ.展开更多
In this paper,we consider the initial-boundary value problem for the large scale three-dimensional(3D)viscous primitive equations under random force.Assuming that the random force and the heat source satisfy the some ...In this paper,we consider the initial-boundary value problem for the large scale three-dimensional(3D)viscous primitive equations under random force.Assuming that the random force and the heat source satisfy the some assumptions,we firstly establish rigorous a priori bounds with coefficients which depend only on boundary data,initial data and the geometry of the problem,and then with the aid of these a priori bounds,the continuous dependence of the solution on changes in the heat source is obtained.展开更多
In this paper, we derive the continuous dependence on the initial-time geometry for the solution of a parabolic equation from dynamo theory. The forward in time problem and backward in time problem are considered. An ...In this paper, we derive the continuous dependence on the initial-time geometry for the solution of a parabolic equation from dynamo theory. The forward in time problem and backward in time problem are considered. An explicit continuous dependence inequality is obtained even with different prescribed data.展开更多
In this paper, we establish the structural stability for the linear differential equations of thermo-diffusion in a semi-infinite pipe flow. Using the technology of a second-order differential inequality, we prove the...In this paper, we establish the structural stability for the linear differential equations of thermo-diffusion in a semi-infinite pipe flow. Using the technology of a second-order differential inequality, we prove the continuous dependence on the density <i><span style="white-space:nowrap;"><i>ρ</i></span></i> and the coefficient of thermal conductivity <i>K</i>. These results show that small changes for these coefficients can’t cause tremendous changes for the solutions.展开更多
Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continu...Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.展开更多
A new update strategy, distance-based update strategy, is presented in Location Dependent Continuous Query (LDCQ) under error limitation. There are different possibilities to intersect when the distances between movin...A new update strategy, distance-based update strategy, is presented in Location Dependent Continuous Query (LDCQ) under error limitation. There are different possibilities to intersect when the distances between moving objects and the querying boundary are different.Therefore, moving objects have different influences to the query result. We set different deviation limits for different moving objects according to distances. A great number of unnecessary updates are reduced and the payload of the system is relieved.展开更多
In this paper we study solutions to a forward Dynamo equation depending continuously on the velocity on an exterior domain,using Logarithmic Convexity Methods.We obtain some more weaker conditions by introducing the u...In this paper we study solutions to a forward Dynamo equation depending continuously on the velocity on an exterior domain,using Logarithmic Convexity Methods.We obtain some more weaker conditions by introducing the unbounded domain.展开更多
In this paper, we derive the continuous dependence on the terminal condition of solutions to nonlinear reflected backward stochastic differential equations involving the subdifferential operator convex function under ...In this paper, we derive the continuous dependence on the terminal condition of solutions to nonlinear reflected backward stochastic differential equations involving the subdifferential operator convex function under non-Lipschitz of a lower semi-continuous, proper and condition by means of the corollary of Bihari inequality.展开更多
COVID-19 epidemic models with constant transmission rate cannot capture the patterns of the infection data in the presence of pharmaceutical and non-pharmaceutical interventions during a pandemic.Because of this,a new...COVID-19 epidemic models with constant transmission rate cannot capture the patterns of the infection data in the presence of pharmaceutical and non-pharmaceutical interventions during a pandemic.Because of this,a new modification of SIR model that contain the vaccination compartment with time dependent coefficients and weak/lossimmunity is explored.Literature review confirms that the effect of vaccination on the time dependent transmission rate is still an open problem.This study answers this open problem.In this study,we first prove the well-posedness and investigate the model dynamics to show their continuous dependence on the model parameters.We then provide an algorithm to derive the time-dependent transmission function for the epidemiologic model and the data of the infected cases.The derived coupled nonlinear differential equations show the effect of vaccination on the transmission rate.Unlike previous studies,we first filter the published data and solve the nonlinear coupled differential equations using the finite difference technique,where the coefficient of the coupled nonlinear differential equations is a function of given data.We then show that time-dependent transmission function can be represented by linear combinations of Gaussian radial base function.We then validate the prediction of our models using numerical simulations,where we used the published data of COVID-19 confirmed cases by the Ministries of Health in Saudi Arabia and Poland.Finally,the numerical solutions of a SIRVI model with time dependent transmission rate show that the waves for currently active cases are in good agreement with the data of Saudi Arabia and Poland.展开更多
The time-dependent Navier-Stokes equations with leak boundary conditions are investigated in this paper. The equivalent variational inequality is derived, and the weak and strong solvabilities of this variational ineq...The time-dependent Navier-Stokes equations with leak boundary conditions are investigated in this paper. The equivalent variational inequality is derived, and the weak and strong solvabilities of this variational inequality are obtained by the Galerkin approximation method and the regularized method. In addition, the continuous dependence property of solutions on given initial data is establisbed, from which the strong solution is unique.展开更多
The aim of this paper is to establish some new discrete inequalities in two independent variables which can be used as handy tools.in the theory of certain fourth order partial finite difference equations. The analys...The aim of this paper is to establish some new discrete inequalities in two independent variables which can be used as handy tools.in the theory of certain fourth order partial finite difference equations. The analysis used in the proof is elementary and the results established provide new estimates for these types of inequalities.AMS (MOS) Subject Classification (1991 ): Primary 26D15.展开更多
A new general class of retarded functional differential equations(that is,RFDEs) with unbounded delay and with finite memory is introduced. The basic theories of existence, uniqueness, continuation, and continuous dep...A new general class of retarded functional differential equations(that is,RFDEs) with unbounded delay and with finite memory is introduced. The basic theories of existence, uniqueness, continuation, and continuous dependence are developed.展开更多
The linear dynamic theory of microstretch thermomagnetoelectroelasticity is studied in this paper.First,a reciprocity relation which involves two processes at different instants is established to form the basis of a u...The linear dynamic theory of microstretch thermomagnetoelectroelasticity is studied in this paper.First,a reciprocity relation which involves two processes at different instants is established to form the basis of a uniqueness result and a reciprocal theorem.The proof of the reciprocal theorem avoids both using the Laplace transform and incorporating the initial conditions into the equations of motion.The uniqueness theorem is derived with no definiteness assumption on the elastic constitutive coefficients.Then the continuous dependence theorem is discussed upon two external data systems.Finally,the variational principle of Hamilton type which fully characterizes the solution of the mixed boundary-initial-value problem（mixed problem） is obtained.These theorems lay a solid foundation for further theoretical and numerical studies on microstretch thermomagnetoelectroelastic materials.展开更多
文摘In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.
文摘The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf- ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.
基金Supported by the National Natural Science Foundation of China(10771171)Supported by the 555 Innovation Talent Project of Gansu Province(GS-555-CXRC)+1 种基金Supported by the Technique Innovation Project of Northwest Normal University(NWNU-KJCXGC-212)Supported by the Youth Foundation of Dingxi Advanced Teachers College(1333)
文摘The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.
基金supported by the National Research Foundation of Korea (NRF) (No.2010-0012215)
文摘This paper investigates the asymptotic behavior of end effects for a Stokes flow defined on a three-dimensional semi-infinite cylinder. With homogeneous Dirichlet conditions of the velocity on the lateral surface of the cylinder, solutions either grow or decay exponentially in the distance from the finite end of the cylinder. In the case of decay, the effect of perturbing the equation parameters is also investigated.
基金The NSF (10271095) of China and NWNU-KJCXGC-212.
文摘The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations.
文摘Reference [1] deals with the uniqueness of solution to problem （A） and solution of problem （A） is continuously dependent on free term and initial value under certain conditions. This paper discuss the solution of problem （A） is continuously dependent on boundary value on the basis of references [2] and [3].
基金Supported by National Natural Science Foundation of China(Grant No.11971123).
文摘The structural stability for the Brinkman-Forchheimer equations with temperature-dependent solubility in a bounded region in R3 was studied.The reaction boundary conditions for the temperature T and the salt concentration were imposed.With the aid of some useful a priori bounds,we were able to demonstrate the continuous dependence result for the Forchheimer coefficient λ.
基金Supported by Innovation Team Project of Humanities and Social Sciences in Colleges and Universities of Guangdong Province(Grant No.2020wcxtd008)Research Team Project Funding of Guangzhou Huashang college(Grant No.2021HSKT01).
文摘In this paper,we consider the initial-boundary value problem for the large scale three-dimensional(3D)viscous primitive equations under random force.Assuming that the random force and the heat source satisfy the some assumptions,we firstly establish rigorous a priori bounds with coefficients which depend only on boundary data,initial data and the geometry of the problem,and then with the aid of these a priori bounds,the continuous dependence of the solution on changes in the heat source is obtained.
文摘In this paper, we derive the continuous dependence on the initial-time geometry for the solution of a parabolic equation from dynamo theory. The forward in time problem and backward in time problem are considered. An explicit continuous dependence inequality is obtained even with different prescribed data.
文摘In this paper, we establish the structural stability for the linear differential equations of thermo-diffusion in a semi-infinite pipe flow. Using the technology of a second-order differential inequality, we prove the continuous dependence on the density <i><span style="white-space:nowrap;"><i>ρ</i></span></i> and the coefficient of thermal conductivity <i>K</i>. These results show that small changes for these coefficients can’t cause tremendous changes for the solutions.
基金Project supported by D.G.E.S. Pb 96-1338-CO 2-01 and the Junta de Andalucia
文摘Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.
文摘A new update strategy, distance-based update strategy, is presented in Location Dependent Continuous Query (LDCQ) under error limitation. There are different possibilities to intersect when the distances between moving objects and the querying boundary are different.Therefore, moving objects have different influences to the query result. We set different deviation limits for different moving objects according to distances. A great number of unnecessary updates are reduced and the payload of the system is relieved.
基金supported by the Foundation of Fujian Education Bureau (0030-826156JB08024)
文摘In this paper we study solutions to a forward Dynamo equation depending continuously on the velocity on an exterior domain,using Logarithmic Convexity Methods.We obtain some more weaker conditions by introducing the unbounded domain.
基金the Key Science and Technology Project of Ministry of Education (207047)The Research Project for Younger Teacher of Anhui Normal University (no.2006xqn49)+2 种基金The Special Project Grants of Anhui Normal University (2006xzx08)The Project Grants for Ph.D of Anhui Normal UniversityThe Teaching Research Project of Anhui Normal University
文摘In this paper, we derive the continuous dependence on the terminal condition of solutions to nonlinear reflected backward stochastic differential equations involving the subdifferential operator convex function under non-Lipschitz of a lower semi-continuous, proper and condition by means of the corollary of Bihari inequality.
基金funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University through Research Group no.RG-21-09-16.
文摘COVID-19 epidemic models with constant transmission rate cannot capture the patterns of the infection data in the presence of pharmaceutical and non-pharmaceutical interventions during a pandemic.Because of this,a new modification of SIR model that contain the vaccination compartment with time dependent coefficients and weak/lossimmunity is explored.Literature review confirms that the effect of vaccination on the time dependent transmission rate is still an open problem.This study answers this open problem.In this study,we first prove the well-posedness and investigate the model dynamics to show their continuous dependence on the model parameters.We then provide an algorithm to derive the time-dependent transmission function for the epidemiologic model and the data of the infected cases.The derived coupled nonlinear differential equations show the effect of vaccination on the transmission rate.Unlike previous studies,we first filter the published data and solve the nonlinear coupled differential equations using the finite difference technique,where the coefficient of the coupled nonlinear differential equations is a function of given data.We then show that time-dependent transmission function can be represented by linear combinations of Gaussian radial base function.We then validate the prediction of our models using numerical simulations,where we used the published data of COVID-19 confirmed cases by the Ministries of Health in Saudi Arabia and Poland.Finally,the numerical solutions of a SIRVI model with time dependent transmission rate show that the waves for currently active cases are in good agreement with the data of Saudi Arabia and Poland.
基金Supported by the National Natural Science Foundation of China(No.50306019,No.10571142,No.10471110,No.10471109)
文摘The time-dependent Navier-Stokes equations with leak boundary conditions are investigated in this paper. The equivalent variational inequality is derived, and the weak and strong solvabilities of this variational inequality are obtained by the Galerkin approximation method and the regularized method. In addition, the continuous dependence property of solutions on given initial data is establisbed, from which the strong solution is unique.
文摘The aim of this paper is to establish some new discrete inequalities in two independent variables which can be used as handy tools.in the theory of certain fourth order partial finite difference equations. The analysis used in the proof is elementary and the results established provide new estimates for these types of inequalities.AMS (MOS) Subject Classification (1991 ): Primary 26D15.
文摘A new general class of retarded functional differential equations(that is,RFDEs) with unbounded delay and with finite memory is introduced. The basic theories of existence, uniqueness, continuation, and continuous dependence are developed.
基金Project supported by the National Natural Science Fundation of China(Nos.11572358 and 11272223)the Training Program for Leading Talent in University Innovative Research Team in Hebei Province(No.LJRC006)
文摘The linear dynamic theory of microstretch thermomagnetoelectroelasticity is studied in this paper.First,a reciprocity relation which involves two processes at different instants is established to form the basis of a uniqueness result and a reciprocal theorem.The proof of the reciprocal theorem avoids both using the Laplace transform and incorporating the initial conditions into the equations of motion.The uniqueness theorem is derived with no definiteness assumption on the elastic constitutive coefficients.Then the continuous dependence theorem is discussed upon two external data systems.Finally,the variational principle of Hamilton type which fully characterizes the solution of the mixed boundary-initial-value problem（mixed problem） is obtained.These theorems lay a solid foundation for further theoretical and numerical studies on microstretch thermomagnetoelectroelastic materials.
