The paper is concerned with the multiplicity of solutions for some nonlinear elliptic equations involving critical Sobolev exponents and mixed boundary conditions.
In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower...In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.展开更多
In this paper, we prove an important existence and uniqueness theorem for a fractional order Fredholm – Volterra integro-differential equation with non-local and global boundary conditions by converting it to the cor...In this paper, we prove an important existence and uniqueness theorem for a fractional order Fredholm – Volterra integro-differential equation with non-local and global boundary conditions by converting it to the corresponding well known Fredholm integral equation of second kind. The considered in this paper has been solved already numerically in [1].展开更多
In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary condit...In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.展开更多
In the poper, the method of separating singularity is applied to study the uniformly difference scheme of a singular perturbation problem for a semilinear ordinary differential equation with mixed boundary value condi...In the poper, the method of separating singularity is applied to study the uniformly difference scheme of a singular perturbation problem for a semilinear ordinary differential equation with mixed boundary value condition. The uniform convergence on small parameter ε of order one for an IVin type difference scheme constructed is proved. At the end of the paper, a numerical example is given. The computing results coincide with the theoretical analysis.展开更多
The stationary and nonstationary rotating Navier-Stokes equations with mixed boundary conditions are investigated in this paper. The existence and uniqueness of the solutions are obtained by the Galerkin approximation...The stationary and nonstationary rotating Navier-Stokes equations with mixed boundary conditions are investigated in this paper. The existence and uniqueness of the solutions are obtained by the Galerkin approximation method. Next, θ-scheme of operator splitting algorithm is applied to rotating Navier-Stokes equations and two subproblems are derived. Finally, the computational algorithms for these subproblems are provided.展开更多
This paper establishes a global Carleman inequality of parabolic equations with mixed boundary conditions and an estimate of the solution. Further, we prove exact controllability of the equation by controls acting on ...This paper establishes a global Carleman inequality of parabolic equations with mixed boundary conditions and an estimate of the solution. Further, we prove exact controllability of the equation by controls acting on an arbitrarily given subdomain or subboundary.展开更多
The solution of boundary value problems(BVP)for fourth order differential equations by their reduction to BVP for second order equations,with the aim to use the available efficient algorithms for the latter ones,attra...The solution of boundary value problems(BVP)for fourth order differential equations by their reduction to BVP for second order equations,with the aim to use the available efficient algorithms for the latter ones,attracts attention from many researchers.In this paper,using the technique developed by the authors in recent works we construct iterative method for a problem with complicated mixed boundary conditions for biharmonic equation which is originated from nanofluidic physics.The convergence rate of the method is proved and some numerical experiments are performed for testing its dependence on a parameter appearing in boundary conditions and on the position of the point where a transmission of boundary conditions occurs.展开更多
We present a proof of the discrete maximum principle(DMP)for the 1D Poisson equation−u"=f equipped with mixed Dirichlet-Neumann boundary conditions.The problem is discretized using finite elements of arbitrary le...We present a proof of the discrete maximum principle(DMP)for the 1D Poisson equation−u"=f equipped with mixed Dirichlet-Neumann boundary conditions.The problem is discretized using finite elements of arbitrary lengths and polynomial degrees(hp-FEM).We show that the DMP holds on all meshes with no limitations to the sizes and polynomial degrees of the elements.展开更多
A robust and general solver for Laplace＇s equation on the interior of a simply connected domain in the plane is described and tested. The solver handles general piecewise smooth domains and Dirichlet, Neumann, and Ro...A robust and general solver for Laplace＇s equation on the interior of a simply connected domain in the plane is described and tested. The solver handles general piecewise smooth domains and Dirichlet, Neumann, and Robin boundary conditions. It is based on an integral equation formulation of the problem. Difficulties due to changes in boundary conditions and corners, cusps, or other examples of non-smoothness of the boundary are handled using a recent technique called recursive compressed inverse preconditioning. The result is a rapid and very accurate solver which is general in scope, its performance is demonstrated via some challenging numerical tests.展开更多
The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixe...The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.展开更多
Some successful vapor-liquid equilibrium(VLE) mixing rules based on excess free energy models proposed in recent years combines the advantages owned partially by equations of state and activity coefficient models to o...Some successful vapor-liquid equilibrium(VLE) mixing rules based on excess free energy models proposed in recent years combines the advantages owned partially by equations of state and activity coefficient models to obtain the better prediction for nonpolar and polar systems.The paper coupled with the merits of MHV1 mixing rule, LCVM mixing rule and WS mixing rule to put forward the new two-parameter mixing rule which satisfies the second viral coefficient boundary condition.The new mixing rule, coupled with the PR equation of state and the NRTL model is tested against 18 kinds of vapor-liquid equilibrium data of nonpolar, nonpolar-polar/polar-nonpolar,and polar-polar systems.The test results indicate that the new model can yield better prediction.Compared to the other two mixing rules (WS,MHV1), the new model shows better VLE prediction capabilities of binary mixtures.展开更多
文摘The paper is concerned with the multiplicity of solutions for some nonlinear elliptic equations involving critical Sobolev exponents and mixed boundary conditions.
基金National Natural Science Foundation of China(No.11271372)Hunan Provincial National Natural Science Foundation of China(No.12JJ2004)Central South University Graduate Innovation Project,China(No.2014zzts136)
文摘In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.
文摘In this paper, we prove an important existence and uniqueness theorem for a fractional order Fredholm – Volterra integro-differential equation with non-local and global boundary conditions by converting it to the corresponding well known Fredholm integral equation of second kind. The considered in this paper has been solved already numerically in [1].
文摘In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.
文摘In the poper, the method of separating singularity is applied to study the uniformly difference scheme of a singular perturbation problem for a semilinear ordinary differential equation with mixed boundary value condition. The uniform convergence on small parameter ε of order one for an IVin type difference scheme constructed is proved. At the end of the paper, a numerical example is given. The computing results coincide with the theoretical analysis.
基金the National Nature Science Foundation of China (Grants No.50306019,No.10571142,No.10471110 and No.10471109)
文摘The stationary and nonstationary rotating Navier-Stokes equations with mixed boundary conditions are investigated in this paper. The existence and uniqueness of the solutions are obtained by the Galerkin approximation method. Next, θ-scheme of operator splitting algorithm is applied to rotating Navier-Stokes equations and two subproblems are derived. Finally, the computational algorithms for these subproblems are provided.
文摘This paper establishes a global Carleman inequality of parabolic equations with mixed boundary conditions and an estimate of the solution. Further, we prove exact controllability of the equation by controls acting on an arbitrarily given subdomain or subboundary.
基金support from Vietnam National Foundation for Science and Technology Development(NAFOSTED)would like to thank the referees for the helpful suggestions.
文摘The solution of boundary value problems(BVP)for fourth order differential equations by their reduction to BVP for second order equations,with the aim to use the available efficient algorithms for the latter ones,attracts attention from many researchers.In this paper,using the technique developed by the authors in recent works we construct iterative method for a problem with complicated mixed boundary conditions for biharmonic equation which is originated from nanofluidic physics.The convergence rate of the method is proved and some numerical experiments are performed for testing its dependence on a parameter appearing in boundary conditions and on the position of the point where a transmission of boundary conditions occurs.
基金the support of the Czech Science Foundation,proj-ects No.102/07/0496 and 102/05/0629the Grant Agency of the Academy of Sciences of the Czech Republic,project No.IAA100760702the Academy of Sciences of the Czech Republic,Institutional Research Plan No.AV0Z10190503。
文摘We present a proof of the discrete maximum principle(DMP)for the 1D Poisson equation−u"=f equipped with mixed Dirichlet-Neumann boundary conditions.The problem is discretized using finite elements of arbitrary lengths and polynomial degrees(hp-FEM).We show that the DMP holds on all meshes with no limitations to the sizes and polynomial degrees of the elements.
文摘A robust and general solver for Laplace＇s equation on the interior of a simply connected domain in the plane is described and tested. The solver handles general piecewise smooth domains and Dirichlet, Neumann, and Robin boundary conditions. It is based on an integral equation formulation of the problem. Difficulties due to changes in boundary conditions and corners, cusps, or other examples of non-smoothness of the boundary are handled using a recent technique called recursive compressed inverse preconditioning. The result is a rapid and very accurate solver which is general in scope, its performance is demonstrated via some challenging numerical tests.
基金Supported by the National Basic Research Program of China(973 Program)(No.2012CB025904)the National Natural Science Foundation of China(No.90916027)
文摘The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.
文摘Some successful vapor-liquid equilibrium(VLE) mixing rules based on excess free energy models proposed in recent years combines the advantages owned partially by equations of state and activity coefficient models to obtain the better prediction for nonpolar and polar systems.The paper coupled with the merits of MHV1 mixing rule, LCVM mixing rule and WS mixing rule to put forward the new two-parameter mixing rule which satisfies the second viral coefficient boundary condition.The new mixing rule, coupled with the PR equation of state and the NRTL model is tested against 18 kinds of vapor-liquid equilibrium data of nonpolar, nonpolar-polar/polar-nonpolar,and polar-polar systems.The test results indicate that the new model can yield better prediction.Compared to the other two mixing rules (WS,MHV1), the new model shows better VLE prediction capabilities of binary mixtures.
基金Supported by by National Natural Science Foundation of China(11071053)the Natural Science Foundation of Hebei Province(A2010001482)the Key Project of Science and Research of Hebei Education Department(ZH2012080)
基金Supported by the National Natural Science Foundation of China(11071053)the Natural Science Foundation of Hebei Province(A2010001482)the Project of Science and Research of Hebei Education Department(the second round in 2010)
