This paper is concerned with the evolutionary p-Laplacian with interior and boundary sources.The critical exponents for the nonlinear sources are determined.
This article is devoted to the discussion of large time behaviour of solutions for viscous Cahn-Hilliard equation with spatial dimension n 〈 5. Some results on global existence of weak solutions for small initial val...This article is devoted to the discussion of large time behaviour of solutions for viscous Cahn-Hilliard equation with spatial dimension n 〈 5. Some results on global existence of weak solutions for small initial value and blow-up of solutions for any nontrivial initial value are established.展开更多
In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um ＋ yup = 0,where γ≥0,m〉 1and P〉m＋2/N We will show that if γ...In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um ＋ yup = 0,where γ≥0,m〉 1and P〉m＋2/N We will show that if γ=0 and 0〈μ〈 2N/n（m-1）＋2 or γ 〉 0 and 1/p-1 〈 μ 〈 2N/N（m-1）＋2 then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S（RN）, there exists an initial-value u0 ∈ C（RN） with limx→∞ uo（x）= 0 such that φ is an w-limit point of the rescaled solutions tμ/2u（tβ, t）, Where β = 2-μ（m-1）/4.展开更多
An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function...An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by Jacobi elliptic functions for the coupled KdV equations are derived. In the limit cases, the solitary wave solutions and the other type of travelling wave solutions for the system are also obtained.展开更多
Adhesive forces exist between soil and the surfaces of soil-engaging components; they increase working resistance and energy consumption. This paper tries to find an approach to reduce the adhesion and resistance of b...Adhesive forces exist between soil and the surfaces of soil-engaging components; they increase working resistance and energy consumption. This paper tries to find an approach to reduce the adhesion and resistance of bulldozing plate. A simplified mechanical model of adhesion and resistance between soil and a non-smooth bulldozing plate is proposed. The interaction force between moist soil and a non-smooth bulldozing plate is analyzed. The pressure and friction distribution on the bulldozing plate are computed, and the anti-adhesive effect of a corrugated bulldozing plate is simulated numerically. Numerical results show that the wavy bulldozing plate achieves an effective drag reduction in moist soil. The optimal wavy shape of the corrugated bulldozing plate with the minimal resistance is designed. The basic principle of reducing soil adhesion of the non-smooth surface is discovered.展开更多
This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration equations ｜x｜λ＋Эt^-Эu=div（｜x｜^k∨u^m）＋｜x｜λ＋ku^p with 0 〈 m 〈...This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration equations ｜x｜λ＋Эt^-Эu=div（｜x｜^k∨u^m）＋｜x｜λ＋ku^p with 0 〈 m 〈 1,p 〉 1,λ≥0, k ∈ R. An interesting phenomenon is that there exist two thresholds k∞ and kl for the exponent k, such that the critical Fujita exponent pc for p exists and is finite if k E （k∞, k1）, otherwise, pc is infinite or does not exist.展开更多
We formulate a lattice Boltzmann model which simulates Korteweg-de Vries equation by using a method of higher moments of lattice Boltzmann equation.Using a series of lattice Boltzmann equations in different time scale...We formulate a lattice Boltzmann model which simulates Korteweg-de Vries equation by using a method of higher moments of lattice Boltzmann equation.Using a series of lattice Boltzmann equations in different time scales and the conservation law in time scale t0,we obtain equilibrium distribution function.The numerical examples show that the method can be used to simulate soliton.展开更多
The author considers the Feigenbaum's functional equation fp(λx) = λf(x) for each p > 2. The existence of nonsingle-valley continuous solutions to this equation is discussed and a feasible method to construct...The author considers the Feigenbaum's functional equation fp(λx) = λf(x) for each p > 2. The existence of nonsingle-valley continuous solutions to this equation is discussed and a feasible method to construct such solutions is given.展开更多
We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vec...We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vector and an ami-symmetric null vector. In particular, we show the existence of a turning point path and a pitchfork point path passing ihrough the double fold point and they are the only singular points nearby. Their nondegeneracy is confirmed. A supporting numerical example is also provided. The main tools for our analysis as well as the compulation are some extended systems.展开更多
In this paper the existence of solutions of the singularly perturbed boundary value problems on infinite interval for the second order nonlinear equation containing a small parameterε>0,εy'=f(x,y,y'),y...In this paper the existence of solutions of the singularly perturbed boundary value problems on infinite interval for the second order nonlinear equation containing a small parameterε>0,εy'=f(x,y,y'),y'(0)=a,y(∞)=βis examined,where are constants,and i=0,1.Moreover,asymptotic estimates of the solutions for the above problems are given.展开更多
The purpose of this paper is to study the superconvergence properties of Ritz-Volterra projection.Through construction a new type of Green function and making use of its properties and the principle of duality,the pap...The purpose of this paper is to study the superconvergence properties of Ritz-Volterra projection.Through construction a new type of Green function and making use of its properties and the principle of duality,the paper proves that the Ritz-Volterra projection defined on r-1 order finite element spaces of Lagrange type in one and two space variable cases possesses O(h2r^2)order and O(h4+1|Inh|)order nodal superconvergence,respectively,and the same type of superconver-gence results are demonstrated for the semidiscrete finite dement approximate solutions of Soboleve-quations.展开更多
We develop an equivalence between the diagonal slices and the perpendicular slices of 3D Young diagrams via Maya diagrams. Furthermore, we construct the fermion representation of quantum toroidal algebra on the 3D You...We develop an equivalence between the diagonal slices and the perpendicular slices of 3D Young diagrams via Maya diagrams. Furthermore, we construct the fermion representation of quantum toroidal algebra on the 3D Young diagrams perpendicularly sliced.展开更多
Let f ： Ω→Gr（n,H） be a holomorphic curve, where Ω is a bounded open simple connected domain on the complex plane C and Gr（n,H） the Grassmannian manifold. Denote by Ef the ＂pull back＂ bundle induced by f. We ...Let f ： Ω→Gr（n,H） be a holomorphic curve, where Ω is a bounded open simple connected domain on the complex plane C and Gr（n,H） the Grassmannian manifold. Denote by Ef the ＂pull back＂ bundle induced by f. We show the uniqueness of the orthogonal decomposition for those complex bundles. As a direct application, we give a complete description of the HIR decomposition of a Cowen- Douglas operator T ∈ Bn（Ω）. Moreover, we compute the maximal self-adjoint subalgebra of A＇（Ef） and A＇（T） respectively. Finally, we fix the masa of A＇（Ef） and .A＇ （T） which depends on the HIR decomposition of Ef or T respectively.展开更多
Applying the theory of Grbner basis to the Schubert presentation for the cohomology of Grassmannians [2], we extend the homology rigidity results known for the classical Grassmanians to the exceptional cases.
In this paper, we show the existence of the renormalized solutions and the entropy solutions of a class of strongly degenerate quasilinear parabolic equations.
In this paper, by the method of upper and lower solutions, we establish the existence of the non-trivial nonnegative periodic solutions for a class of degenerate diffusion system arising from dynamics of biological gr...In this paper, by the method of upper and lower solutions, we establish the existence of the non-trivial nonnegative periodic solutions for a class of degenerate diffusion system arising from dynamics of biological groups.展开更多
Let w be the element of maximal length in a finite irreducible Coxeter system （W, S）. In the present paper, we get the length of w when （W, S） is of type An, Bn/Cn or Dn.
Let X be a compact metric space containing at least two points and let f ： X → X be continuous. In this paper, we introduce the notion of totally maximum sensitive （TMS, for short） and prove that f is weakly mixin...Let X be a compact metric space containing at least two points and let f ： X → X be continuous. In this paper, we introduce the notion of totally maximum sensitive （TMS, for short） and prove that f is weakly mixing if and only if it is TMS, and if X = [0, 1], then f is weakly mixing if and only if it is 2-maximum sensitive.展开更多
In this paper existence,uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameter are exam...In this paper existence,uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameter are examined,where are constants,and i=0,1.展开更多
基金supported by NSFCResearch Fundfor the Doctoral Program of Higher Education of China,Fundamental Research Project of Jilin University(200903284)Graduate Innovation Fund of Jilin University(20101045)
文摘This paper is concerned with the evolutionary p-Laplacian with interior and boundary sources.The critical exponents for the nonlinear sources are determined.
文摘This article is devoted to the discussion of large time behaviour of solutions for viscous Cahn-Hilliard equation with spatial dimension n 〈 5. Some results on global existence of weak solutions for small initial value and blow-up of solutions for any nontrivial initial value are established.
基金supported by National Natural Science Foundation of Chinasupported by Specialized Research Fund for the Doctoral Program of Higher Educationsupported by Graduate Innovation Fund of Jilin University (20101045)
文摘In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um ＋ yup = 0,where γ≥0,m〉 1and P〉m＋2/N We will show that if γ=0 and 0〈μ〈 2N/n（m-1）＋2 or γ 〉 0 and 1/p-1 〈 μ 〈 2N/N（m-1）＋2 then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S（RN）, there exists an initial-value u0 ∈ C（RN） with limx→∞ uo（x）= 0 such that φ is an w-limit point of the rescaled solutions tμ/2u（tβ, t）, Where β = 2-μ（m-1）/4.
基金Project supported by the Natural Science Foundation of Henan Province of China （Grant No 0111050200） and the Science Foundation of Henan University of Science and Technology （Grant Nos 2004ZY040 and 2004ZD002）.
文摘An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by Jacobi elliptic functions for the coupled KdV equations are derived. In the limit cases, the solitary wave solutions and the other type of travelling wave solutions for the system are also obtained.
文摘Adhesive forces exist between soil and the surfaces of soil-engaging components; they increase working resistance and energy consumption. This paper tries to find an approach to reduce the adhesion and resistance of bulldozing plate. A simplified mechanical model of adhesion and resistance between soil and a non-smooth bulldozing plate is proposed. The interaction force between moist soil and a non-smooth bulldozing plate is analyzed. The pressure and friction distribution on the bulldozing plate are computed, and the anti-adhesive effect of a corrugated bulldozing plate is simulated numerically. Numerical results show that the wavy bulldozing plate achieves an effective drag reduction in moist soil. The optimal wavy shape of the corrugated bulldozing plate with the minimal resistance is designed. The basic principle of reducing soil adhesion of the non-smooth surface is discovered.
文摘This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration equations ｜x｜λ＋Эt^-Эu=div（｜x｜^k∨u^m）＋｜x｜λ＋ku^p with 0 〈 m 〈 1,p 〉 1,λ≥0, k ∈ R. An interesting phenomenon is that there exist two thresholds k∞ and kl for the exponent k, such that the critical Fujita exponent pc for p exists and is finite if k E （k∞, k1）, otherwise, pc is infinite or does not exist.
基金Supported by the Foundation of the Laboratory for Nonlinear Mechanics of Continuous Media,Institute of Mechanics,Chinese Academy of Sciences.
文摘We formulate a lattice Boltzmann model which simulates Korteweg-de Vries equation by using a method of higher moments of lattice Boltzmann equation.Using a series of lattice Boltzmann equations in different time scales and the conservation law in time scale t0,we obtain equilibrium distribution function.The numerical examples show that the method can be used to simulate soliton.
文摘The author considers the Feigenbaum's functional equation fp(λx) = λf(x) for each p > 2. The existence of nonsingle-valley continuous solutions to this equation is discussed and a feasible method to construct such solutions is given.
文摘We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vector and an ami-symmetric null vector. In particular, we show the existence of a turning point path and a pitchfork point path passing ihrough the double fold point and they are the only singular points nearby. Their nondegeneracy is confirmed. A supporting numerical example is also provided. The main tools for our analysis as well as the compulation are some extended systems.
文摘In this paper the existence of solutions of the singularly perturbed boundary value problems on infinite interval for the second order nonlinear equation containing a small parameterε>0,εy'=f(x,y,y'),y'(0)=a,y(∞)=βis examined,where are constants,and i=0,1.Moreover,asymptotic estimates of the solutions for the above problems are given.
文摘The purpose of this paper is to study the superconvergence properties of Ritz-Volterra projection.Through construction a new type of Green function and making use of its properties and the principle of duality,the paper proves that the Ritz-Volterra projection defined on r-1 order finite element spaces of Lagrange type in one and two space variable cases possesses O(h2r^2)order and O(h4+1|Inh|)order nodal superconvergence,respectively,and the same type of superconver-gence results are demonstrated for the semidiscrete finite dement approximate solutions of Soboleve-quations.
基金Supported by the Morningside Center of Chinese Academy of Sciences and Kavli Institute for Theoretical Physics of Chinese Academy of Sciences, the National Natural Science Foundation of China under Grant No 11031005, the Beijing Municipal Education Commission Foundation under Grant Nos KZ201210028032 and KM201210028006, and the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No 20121108120005.
文摘We develop an equivalence between the diagonal slices and the perpendicular slices of 3D Young diagrams via Maya diagrams. Furthermore, we construct the fermion representation of quantum toroidal algebra on the 3D Young diagrams perpendicularly sliced.
文摘Let f ： Ω→Gr（n,H） be a holomorphic curve, where Ω is a bounded open simple connected domain on the complex plane C and Gr（n,H） the Grassmannian manifold. Denote by Ef the ＂pull back＂ bundle induced by f. We show the uniqueness of the orthogonal decomposition for those complex bundles. As a direct application, we give a complete description of the HIR decomposition of a Cowen- Douglas operator T ∈ Bn（Ω）. Moreover, we compute the maximal self-adjoint subalgebra of A＇（Ef） and A＇（T） respectively. Finally, we fix the masa of A＇（Ef） and .A＇ （T） which depends on the HIR decomposition of Ef or T respectively.
文摘Applying the theory of Grbner basis to the Schubert presentation for the cohomology of Grassmannians [2], we extend the homology rigidity results known for the classical Grassmanians to the exceptional cases.
基金The NSFC (10626024) of ChinaChina Postdoctoral Science Foundation and Graduate Innovation Lab of Jilin University
文摘In this paper, we show the existence of the renormalized solutions and the entropy solutions of a class of strongly degenerate quasilinear parabolic equations.
文摘In this paper, by the method of upper and lower solutions, we establish the existence of the non-trivial nonnegative periodic solutions for a class of degenerate diffusion system arising from dynamics of biological groups.
文摘Let w be the element of maximal length in a finite irreducible Coxeter system （W, S）. In the present paper, we get the length of w when （W, S） is of type An, Bn/Cn or Dn.
基金The NNSF(10771084)of Chinathe NSP(68[2005])of the Education Department of Jilin Province China.
文摘Let X be a compact metric space containing at least two points and let f ： X → X be continuous. In this paper, we introduce the notion of totally maximum sensitive （TMS, for short） and prove that f is weakly mixing if and only if it is TMS, and if X = [0, 1], then f is weakly mixing if and only if it is 2-maximum sensitive.
文摘In this paper existence,uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameter are examined,where are constants,and i=0,1.
