This paper presents a new strategy of using the radial integration boundary element method （RIBEM） to solve non-homogeneous heat conduction and thermoelasticity problems. In the method, the evaluation of the radial ...This paper presents a new strategy of using the radial integration boundary element method （RIBEM） to solve non-homogeneous heat conduction and thermoelasticity problems. In the method, the evaluation of the radial in-tegral which is used to transform domain integrals to equivalent boundary integrals is carried out on the basis of elemental nodes. As a result, the computational time spent in evaluating domain integrals can be saved considerably in comparison with the conventional RIBEM. Three numerical examples are given to demonstrate the correctness and computational efficiency of the proposed approach.展开更多
In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body...In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.展开更多
In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations {μt-△μ=g（μ）＋λf（x）,（x,t）∈Ω×（0,T）,μ=0,（x,t）∈ Ω×[0,T）...In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations {μt-△μ=g（μ）＋λf（x）,（x,t）∈Ω×（0,T）,μ=0,（x,t）∈ Ω×[0,T）,μ（x,0）=μ0（x）≥0,x∈Ω.By combining a priori estimate of global solution with property of stationary solution set of problem （P）, we prove that the minimal stationary solution Uλ（x） of problem （P） is stable, whereas, any other stationary solution is an initial datum threshold for the existence and nonexistence of global solution to problem （P）.展开更多
In this paper,we discuss the local existence of H^i(i=2,4)solutions for a 1D compressible viscous micropolar fluid model with non-homogeneous temperature boundary.The proof is based on the local existence of solutions...In this paper,we discuss the local existence of H^i(i=2,4)solutions for a 1D compressible viscous micropolar fluid model with non-homogeneous temperature boundary.The proof is based on the local existence of solutions in[1].展开更多
On the basis of similar structure of solutions of ordinary differential equation (ODE) boundary value problem, the similar construction method was put forward by solving problems of fluid flow in porous media through ...On the basis of similar structure of solutions of ordinary differential equation (ODE) boundary value problem, the similar construction method was put forward by solving problems of fluid flow in porous media through the homogeneous reservoir. It is indicate that the pressure distribution of dimensionless reservoir and bottom hole in Laplace space, which take on the radial flow, also shows similar structure, and the internal relationship between the above solutions were illustrated in detail.展开更多
The homogeneous quadratic riemann boundary value problem(1)with H?lder continuous coefficients for the normal case was considered by the author in 1997.But the solutions obtained there are incomplete.Here its general ...The homogeneous quadratic riemann boundary value problem(1)with H?lder continuous coefficients for the normal case was considered by the author in 1997.But the solutions obtained there are incomplete.Here its general method of solution is obtained.展开更多
In this paper,we explore non-homogeneous stochastic linear-quadratic(LQ)optimal control problems with multidimensional states and regime switching.We focus on the corresponding stochastic Riccati equation(SRE),which m...In this paper,we explore non-homogeneous stochastic linear-quadratic(LQ)optimal control problems with multidimensional states and regime switching.We focus on the corresponding stochastic Riccati equation(SRE),which mirrors that of the homogeneous stochastic LQ optimal control problem,and the adjoint backward stochastic differential equation(BSDE),which arises from the non-homogeneous terms in the state equation and cost functional.We solve both the SRE and adjoint BSDE using the contraction mapping method,which helps represent the closed-loop optimal control and the optimal value of our problems.In particular,we extend some results of Hu et al.[7]to the multidimensional case.展开更多
We employ fundamental equations of non-homogeneous elasticity and Fourierintegral transformations to obtain the general solutions of the stress function.On thebasis of these points of view and when the forces on the b...We employ fundamental equations of non-homogeneous elasticity and Fourierintegral transformations to obtain the general solutions of the stress function.On thebasis of these points of view and when the forces on the boundary are arbityary for nonhomogeneous half-plane problems with the Young’s modulus E(x)-E_0θxp[βx].accurate solutions are obtained At last with the degeneracy it is obtained that thefamous Boussnesq solution and this method is successful.展开更多
In this paper, we improve the algorithm and rewrite the function make- Pairing for computing a Gorni-Zampieri pair of a homogeneous polynomial map. As an application, some counterexamples to PLDP （dependence problem ...In this paper, we improve the algorithm and rewrite the function make- Pairing for computing a Gorni-Zampieri pair of a homogeneous polynomial map. As an application, some counterexamples to PLDP （dependence problem for power lin- car maps） are obtained, including one in the lowest dimension （n = 48） in all suchcounterexamples one has found up to now.展开更多
The nucleation process of stick-slip instability was analyzed based on the experimental measurements of strain and fault slip on homogeneous and non-homogeneous faults. The results show that the nucleation process of ...The nucleation process of stick-slip instability was analyzed based on the experimental measurements of strain and fault slip on homogeneous and non-homogeneous faults. The results show that the nucleation process of stick-slip on the homogeneous fault is of weak slip-weakening behavior under constant loading point velocity. The existence of a short "weak segment" on the fault makes slip-weakening phenomenon in nucleation process more obvious, while the existence of a long "weak segment" on the fault makes the nucleation process changed. The nucleation is characterized by accelerating slip in a local region and rapid increase of shear stress along the fault in this case, which is more coincident with the rate and state friction law. During the period when fault is locked, increasing of shear stress causes lateral elastic dilation near the fault, and the rebound of the dilation at the time of instability causes an instantaneous increase of normal stress in the fault plane, which is an important factor making fault be rapidly locked and its strength recovered.展开更多
The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of subline...The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of sublinear operators including Hardy-Littlewood maximal operators,Calderón-Zygmund operators and fractional integral operators.Further- more,some weak estimate of these operators in weak homogeneous Morrey-Herz spaces are also obtained.Moreover,the authors discuss the boundedness in homogeneous Morrey-Herz spaces of the maximal commutators associated with Hardy-Littlewood maximal operators and multilinear commutators generated by Calderón-Zygmund operators or fractional integral operators with RBMO（μ）functions.展开更多
In this article, the convection dominated convection-diffusion problems with the periodic micro-structure are discussed. A two-scale finite element scheme based on the homogenization technique for this kind of problem...In this article, the convection dominated convection-diffusion problems with the periodic micro-structure are discussed. A two-scale finite element scheme based on the homogenization technique for this kind of problems is provided. The error estimates between the exact solution and the approximation solution, of the homogenized equation or the two-scale finite element scheme are analyzed. It is shown that the scheme provided in this article is convergent for any fixed diffusion coefficient 5, and it may be convergent independent of δ under some conditions. The numerical results demonstrating the theoretical results are presented in this article.展开更多
We consider boundary-value problems with rapidly alternating types of boundary conditions. We present the classification of homogenized （limit） problems depending on the ratio of small parameters, which characterize...We consider boundary-value problems with rapidly alternating types of boundary conditions. We present the classification of homogenized （limit） problems depending on the ratio of small parameters, which characterize the diameter of parts of the boundary with different types of boundary conditions. Also we study the respective spectral problem of this type.展开更多
In order to recover unknown space-dependent function G(x)or unknown time-dependent function H(t)in the wave source F(x;t)=G(x)H(t),we develop a technique of homogenized function and differencing equations,which can si...In order to recover unknown space-dependent function G(x)or unknown time-dependent function H(t)in the wave source F(x;t)=G(x)H(t),we develop a technique of homogenized function and differencing equations,which can significantly reduce the difficulty in the inverse wave source recovery problem,only needing to solve a few equations in the problem domain,since the initial condition/boundary conditions and a supplementary final time condition are satisfied automatically.As a consequence,the eigenfunctions are used to expand the trial solutions,and then a small scale linear system is solved to determine the expansion coefficients from the differencing equations.Because the ill-posedness of the inverse wave source problem is greatly reduced,the present method is accurate and stable against a large noise up to 50%,of which the numerical tests confirm the observation.展开更多
The main goal of the paper is to obtain the local strong solution of the Cauchy problem of the nonhomogeneous incompressible Boussinesq equation in two-dimension space. Especially, when the far-field density is vacuum...The main goal of the paper is to obtain the local strong solution of the Cauchy problem of the nonhomogeneous incompressible Boussinesq equation in two-dimension space. Especially, when the far-field density is vacuum, we make a priori estimate in a bound ball and prove the existence and uniqueness of the local strong solution of the Boussinesq equation.展开更多
We investigate the global structures of the non-selfsimilar solutions for n-dimensional(n-D) nonhomogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a(n-1)-...We investigate the global structures of the non-selfsimilar solutions for n-dimensional(n-D) nonhomogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a(n-1)-dimensional sphere. We first obtain the expressions of n-D shock waves and rarefaction waves emitting from the initial discontinuity. Then, by estimating the new kind of interactions of the related elementary waves,we obtain the global structures of the non-selfsimilar solutions, in which ingenious techniques are proposed to construct the n-D shock waves. The asymptotic behaviors with geometric structures are also proved.展开更多
Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Litt...Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Littlewood-Paley g-function gr （r ∈ [2, ∞）） is bounded from Hardy space H1（u） into L1（u）. Moreover, the authors show that, if f ∈ RBMO（u）, then [gr（f）]r is either infinite everywhere or finite almost everywhere, and in the latter case, [gr（f）]r belongs to RBLO（u） with the norm no more than ｜｜f｜｜ RBMO（u） multiplied by a positive constant which is independent of f. As a corollary, the authors obtain the boundedness of gr from RBMO（u） into RBLO（u）. The vector valued Calderon-Zygmund theory over （X, d, u） is also established with details in this paper.展开更多
This paper presents and analyzes a Discrete Duality Finite Volume(DDFV)method to solve 2D diffusion problems under prescribed Robin boundary conditions.The derivation of a symmetric discrete problem is established.The...This paper presents and analyzes a Discrete Duality Finite Volume(DDFV)method to solve 2D diffusion problems under prescribed Robin boundary conditions.The derivation of a symmetric discrete problem is established.The existence and uniqueness of a solution to this discrete problem are shown via the positive definiteness of its associated matrix.We show that the discrete scheme meets the Neumann problem when the parameterα→0(and,in a sense,whenα→∞the Dirichlet problem).This work is a continuation of our work regarding the development of DDFV methods.The main innovation here is taking into account Robin’s boundary conditions.We provide a few steps of Matlab implementation and numerical tests to confirm the effectiveness of the method.展开更多
基金supported by the National Natural Science Foundation of China (10872050, 11172055)the Fundamental Research Funds for the Centred Universities (DUT11ZD(G)01)
文摘This paper presents a new strategy of using the radial integration boundary element method （RIBEM） to solve non-homogeneous heat conduction and thermoelasticity problems. In the method, the evaluation of the radial in-tegral which is used to transform domain integrals to equivalent boundary integrals is carried out on the basis of elemental nodes. As a result, the computational time spent in evaluating domain integrals can be saved considerably in comparison with the conventional RIBEM. Three numerical examples are given to demonstrate the correctness and computational efficiency of the proposed approach.
基金supported by the US ARO grants 49308-MA and 56349-MAthe US AFSOR grant FA9550-06-1-024+1 种基金he US NSF grant DMS-0911434the State Key Laboratory of Scientific and Engineering Computing of Chinese Academy of Sciences during a visit by Z.Li between July-August,2008.
文摘In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.
基金supported by Natural Science Foundation of China(10971061)Hunan Provincial Innovation Foundation For Postgraduate(CX2010B209)
文摘In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations {μt-△μ=g（μ）＋λf（x）,（x,t）∈Ω×（0,T）,μ=0,（x,t）∈ Ω×[0,T）,μ（x,0）=μ0（x）≥0,x∈Ω.By combining a priori estimate of global solution with property of stationary solution set of problem （P）, we prove that the minimal stationary solution Uλ（x） of problem （P） is stable, whereas, any other stationary solution is an initial datum threshold for the existence and nonexistence of global solution to problem （P）.
基金Supported by the NNSF of China(11271066)Supported by the grant of Shanghai Education Commission(13ZZ048)
文摘In this paper,we discuss the local existence of H^i(i=2,4)solutions for a 1D compressible viscous micropolar fluid model with non-homogeneous temperature boundary.The proof is based on the local existence of solutions in[1].
文摘On the basis of similar structure of solutions of ordinary differential equation (ODE) boundary value problem, the similar construction method was put forward by solving problems of fluid flow in porous media through the homogeneous reservoir. It is indicate that the pressure distribution of dimensionless reservoir and bottom hole in Laplace space, which take on the radial flow, also shows similar structure, and the internal relationship between the above solutions were illustrated in detail.
基金Supported by the National Natural Science Foun dation of China(19871064)
文摘The homogeneous quadratic riemann boundary value problem(1)with H?lder continuous coefficients for the normal case was considered by the author in 1997.But the solutions obtained there are incomplete.Here its general method of solution is obtained.
基金Financial support from the National Natural Science Foundation of China(Grant Nos.12101400 and 12326603)is gratefully acknowledged。
文摘In this paper,we explore non-homogeneous stochastic linear-quadratic(LQ)optimal control problems with multidimensional states and regime switching.We focus on the corresponding stochastic Riccati equation(SRE),which mirrors that of the homogeneous stochastic LQ optimal control problem,and the adjoint backward stochastic differential equation(BSDE),which arises from the non-homogeneous terms in the state equation and cost functional.We solve both the SRE and adjoint BSDE using the contraction mapping method,which helps represent the closed-loop optimal control and the optimal value of our problems.In particular,we extend some results of Hu et al.[7]to the multidimensional case.
文摘We employ fundamental equations of non-homogeneous elasticity and Fourierintegral transformations to obtain the general solutions of the stress function.On thebasis of these points of view and when the forces on the boundary are arbityary for nonhomogeneous half-plane problems with the Young’s modulus E(x)-E_0θxp[βx].accurate solutions are obtained At last with the degeneracy it is obtained that thefamous Boussnesq solution and this method is successful.
基金The"985 Project"and"211 Project"of Jilin Universitythe Basis Scientific Research Fund(200903286)of Ministry of Education of China+1 种基金the NSF(11126044,11071097)of ChinaShandong Postdoctoral Science Foundation(201003054),Innovation Program
文摘In this paper, we improve the algorithm and rewrite the function make- Pairing for computing a Gorni-Zampieri pair of a homogeneous polynomial map. As an application, some counterexamples to PLDP （dependence problem for power lin- car maps） are obtained, including one in the lowest dimension （n = 48） in all suchcounterexamples one has found up to now.
文摘The nucleation process of stick-slip instability was analyzed based on the experimental measurements of strain and fault slip on homogeneous and non-homogeneous faults. The results show that the nucleation process of stick-slip on the homogeneous fault is of weak slip-weakening behavior under constant loading point velocity. The existence of a short "weak segment" on the fault makes slip-weakening phenomenon in nucleation process more obvious, while the existence of a long "weak segment" on the fault makes the nucleation process changed. The nucleation is characterized by accelerating slip in a local region and rapid increase of shear stress along the fault in this case, which is more coincident with the rate and state friction law. During the period when fault is locked, increasing of shear stress causes lateral elastic dilation near the fault, and the rebound of the dilation at the time of instability causes an instantaneous increase of normal stress in the fault plane, which is an important factor making fault be rapidly locked and its strength recovered.
基金the North China Electric Power University Youth Foundation(No.200611004)the Renmin University of China Science Research Foundation(No.30206104)
文摘The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of sublinear operators including Hardy-Littlewood maximal operators,Calderón-Zygmund operators and fractional integral operators.Further- more,some weak estimate of these operators in weak homogeneous Morrey-Herz spaces are also obtained.Moreover,the authors discuss the boundedness in homogeneous Morrey-Herz spaces of the maximal commutators associated with Hardy-Littlewood maximal operators and multilinear commutators generated by Calderón-Zygmund operators or fractional integral operators with RBMO（μ）functions.
基金the Special Funds for Major State Basic Research Projects （No.G2000067102） National Natural Science Foundation of China （No.60474027）.
文摘In this article, the convection dominated convection-diffusion problems with the periodic micro-structure are discussed. A two-scale finite element scheme based on the homogenization technique for this kind of problems is provided. The error estimates between the exact solution and the approximation solution, of the homogenized equation or the two-scale finite element scheme are analyzed. It is shown that the scheme provided in this article is convergent for any fixed diffusion coefficient 5, and it may be convergent independent of δ under some conditions. The numerical results demonstrating the theoretical results are presented in this article.
基金supported by the program"Leading Scientific Schools"supported by RFBR
文摘We consider boundary-value problems with rapidly alternating types of boundary conditions. We present the classification of homogenized （limit） problems depending on the ratio of small parameters, which characterize the diameter of parts of the boundary with different types of boundary conditions. Also we study the respective spectral problem of this type.
文摘In order to recover unknown space-dependent function G(x)or unknown time-dependent function H(t)in the wave source F(x;t)=G(x)H(t),we develop a technique of homogenized function and differencing equations,which can significantly reduce the difficulty in the inverse wave source recovery problem,only needing to solve a few equations in the problem domain,since the initial condition/boundary conditions and a supplementary final time condition are satisfied automatically.As a consequence,the eigenfunctions are used to expand the trial solutions,and then a small scale linear system is solved to determine the expansion coefficients from the differencing equations.Because the ill-posedness of the inverse wave source problem is greatly reduced,the present method is accurate and stable against a large noise up to 50%,of which the numerical tests confirm the observation.
文摘The main goal of the paper is to obtain the local strong solution of the Cauchy problem of the nonhomogeneous incompressible Boussinesq equation in two-dimension space. Especially, when the far-field density is vacuum, we make a priori estimate in a bound ball and prove the existence and uniqueness of the local strong solution of the Boussinesq equation.
基金partly supported by the National Natural Science Foundation of China (Grant11701551 and Grant 11971024)partly supported by the National Natural Science Foundation of China (Grant 11471332)。
文摘We investigate the global structures of the non-selfsimilar solutions for n-dimensional(n-D) nonhomogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a(n-1)-dimensional sphere. We first obtain the expressions of n-D shock waves and rarefaction waves emitting from the initial discontinuity. Then, by estimating the new kind of interactions of the related elementary waves,we obtain the global structures of the non-selfsimilar solutions, in which ingenious techniques are proposed to construct the n-D shock waves. The asymptotic behaviors with geometric structures are also proved.
基金Supported by National Natural Science Foundation of China(Grant No.11471040)the Fundamental Research Funds for the Central Universities(Grant No.2014KJJCA10)
文摘Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Littlewood-Paley g-function gr （r ∈ [2, ∞）） is bounded from Hardy space H1（u） into L1（u）. Moreover, the authors show that, if f ∈ RBMO（u）, then [gr（f）]r is either infinite everywhere or finite almost everywhere, and in the latter case, [gr（f）]r belongs to RBLO（u） with the norm no more than ｜｜f｜｜ RBMO（u） multiplied by a positive constant which is independent of f. As a corollary, the authors obtain the boundedness of gr from RBMO（u） into RBLO（u）. The vector valued Calderon-Zygmund theory over （X, d, u） is also established with details in this paper.
文摘This paper presents and analyzes a Discrete Duality Finite Volume(DDFV)method to solve 2D diffusion problems under prescribed Robin boundary conditions.The derivation of a symmetric discrete problem is established.The existence and uniqueness of a solution to this discrete problem are shown via the positive definiteness of its associated matrix.We show that the discrete scheme meets the Neumann problem when the parameterα→0(and,in a sense,whenα→∞the Dirichlet problem).This work is a continuation of our work regarding the development of DDFV methods.The main innovation here is taking into account Robin’s boundary conditions.We provide a few steps of Matlab implementation and numerical tests to confirm the effectiveness of the method.
