Solutions of quasilinear mixed boundary problems for the some parabolic an elliptic partial differential equations are interpreted as solutions of a kind of backward stochastic differential equations, which are associ...Solutions of quasilinear mixed boundary problems for the some parabolic an elliptic partial differential equations are interpreted as solutions of a kind of backward stochastic differential equations, which are associated with the classical Ito forward stochastic differential equations with reflecting boundary conditions.展开更多
This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of suff...This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.展开更多
In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by me...In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.展开更多
The analytical continuation method is adopted to solve a mixed electric boundary value problem for a piezoelectric medium under anti-plane deformation.The crack face is partly conductive and partly impermeable.The res...The analytical continuation method is adopted to solve a mixed electric boundary value problem for a piezoelectric medium under anti-plane deformation.The crack face is partly conductive and partly impermeable.The results show that the stress intensity factor is identical with the mode Ⅲ stress intensity factor independent of the conducting length.But the electric field and the electric displacement are dependent on the electric boundary conditions on the crack faces and are singular not only at the crack tips but also at the junctures between the impermeable part and conducting portions.展开更多
In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of partic...In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system. Three examples are presented to show the stability and high convergence rate of the method.展开更多
We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the f...We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the first part,we obtain the well-posedness of the direct scattering problem by the variational method.In the second part,we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity,and the shape of the external obstacle,however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.展开更多
.In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of....In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary.We show the existence of at least one,two or infinitely many non-trivial weak solutions according to hypotheses on given functions.展开更多
In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are es...In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are established, which improve and generalize the existing results, and play an important role in numerical solutions of partial differential equations. We also develop a lifting technique, with which we could handle mixed inho- mogeneous boundary conditions easily. As examples of applications, spectral schemes are provided for three model problems with mixed inhomogeneous boundary conditions. The spectral accuracy in space of proposed algorithms is proved. Efficient implementations are presented. Numerical results demonstrate their high accuracy, and confirm the theoretical analysis well.展开更多
A probabilistic approach is developed to solve semilinear and generalized mixed boundaryvalue problems involving Schrodinger operators. The results obtained in this paper generalize thecorresponding results of [1] and...A probabilistic approach is developed to solve semilinear and generalized mixed boundaryvalue problems involving Schrodinger operators. The results obtained in this paper generalize thecorresponding results of [1] and partly generalize the result of [2] as well.展开更多
This paper deals with a class of doubly degenerate parabolic equations, including as particular cases the porous medium equation and the degenerate pLaplace equation （p 〉 2）ut-div（b（x,t,u）｜↓△u｜^p-2↓△u）=f...This paper deals with a class of doubly degenerate parabolic equations, including as particular cases the porous medium equation and the degenerate pLaplace equation （p 〉 2）ut-div（b（x,t,u）｜↓△u｜^p-2↓△u）=f（x,u,t）The initial-boundary value problem in a bounded domain of R^N is considered under mixed boundary conditions. The existence of local-in-time weak solutions is obtained.展开更多
This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann con...This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.展开更多
In this paper we discuss the existence of at least three solutions for a class of gradient mixed boundary value systems. The approach is fully based on a recent three critical points theorem of B. Ricceri [A three cri...In this paper we discuss the existence of at least three solutions for a class of gradient mixed boundary value systems. The approach is fully based on a recent three critical points theorem of B. Ricceri [A three critical points theorem revisited, Nonlinear Anal., 70：9（2009）,3084-3089].展开更多
In this paper, the relationship between the time dependent solutions and steady state solutions of the semiconductor equations affected by magnetic field is considered. A decay estimate is proved by a series of est...In this paper, the relationship between the time dependent solutions and steady state solutions of the semiconductor equations affected by magnetic field is considered. A decay estimate is proved by a series of estimates on the solutions under some condition.展开更多
In this paper,we propose the Laguerre spectral method for high order problems with mixed inhomogeneous boundary conditions.It is also available for approximated solutions growing fast at infinity.The spectral accura...In this paper,we propose the Laguerre spectral method for high order problems with mixed inhomogeneous boundary conditions.It is also available for approximated solutions growing fast at infinity.The spectral accuracy is proved.Numerical results demonstrate its high effectiveness.展开更多
The unsteady flow of viscous incompressible shear-thinning non-Newtonian fluid with mixed bound- ary is investigated. The boundary condition on the outflow is the modified natural boundary condition, it con- tains the...The unsteady flow of viscous incompressible shear-thinning non-Newtonian fluid with mixed bound- ary is investigated. The boundary condition on the outflow is the modified natural boundary condition, it con- tains the additional nonlinear term, which enables us to control the kinetic energy of the backward flow. The global existence of weak solution is proved. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.展开更多
In this paper, we investigate a new pseudospectral method for mixed boundary value problems defined on quadrilaterals. We introduce a new Legendre-Gauss type interpolation and establish the basic approximation results...In this paper, we investigate a new pseudospectral method for mixed boundary value problems defined on quadrilaterals. We introduce a new Legendre-Gauss type interpolation and establish the basic approximation results, which play important roles in pseudospectral method for partial differential equations defined on quadrilaterals. We propose pseudospee- tral method for two model problems and prove their spectral accuracy. Numerical results demonstrate their high efficiency. The approximation results developed in this paper are also applicable to other problems defined on complex domains.展开更多
文摘Solutions of quasilinear mixed boundary problems for the some parabolic an elliptic partial differential equations are interpreted as solutions of a kind of backward stochastic differential equations, which are associated with the classical Ito forward stochastic differential equations with reflecting boundary conditions.
文摘This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.
文摘In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.
基金Project supported by the National Natural Science Foundation of China (Nos.10072033 and 10132010).
文摘The analytical continuation method is adopted to solve a mixed electric boundary value problem for a piezoelectric medium under anti-plane deformation.The crack face is partly conductive and partly impermeable.The results show that the stress intensity factor is identical with the mode Ⅲ stress intensity factor independent of the conducting length.But the electric field and the electric displacement are dependent on the electric boundary conditions on the crack faces and are singular not only at the crack tips but also at the junctures between the impermeable part and conducting portions.
基金Partially Supported by the National Natural Science Foundation of China
文摘In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system. Three examples are presented to show the stability and high convergence rate of the method.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China(2019D01A05)supported by the NSFC(11571132)。
文摘We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the first part,we obtain the well-posedness of the direct scattering problem by the variational method.In the second part,we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity,and the shape of the external obstacle,however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.
文摘.In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary.We show the existence of at least one,two or infinitely many non-trivial weak solutions according to hypotheses on given functions.
文摘In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are established, which improve and generalize the existing results, and play an important role in numerical solutions of partial differential equations. We also develop a lifting technique, with which we could handle mixed inho- mogeneous boundary conditions easily. As examples of applications, spectral schemes are provided for three model problems with mixed inhomogeneous boundary conditions. The spectral accuracy in space of proposed algorithms is proved. Efficient implementations are presented. Numerical results demonstrate their high accuracy, and confirm the theoretical analysis well.
基金This project is supported by the National Natural Science Foundation of China
文摘A probabilistic approach is developed to solve semilinear and generalized mixed boundaryvalue problems involving Schrodinger operators. The results obtained in this paper generalize thecorresponding results of [1] and partly generalize the result of [2] as well.
基金The NSFC(10371050)and the"985"program of Jilin University.
文摘This paper deals with a class of doubly degenerate parabolic equations, including as particular cases the porous medium equation and the degenerate pLaplace equation （p 〉 2）ut-div（b（x,t,u）｜↓△u｜^p-2↓△u）=f（x,u,t）The initial-boundary value problem in a bounded domain of R^N is considered under mixed boundary conditions. The existence of local-in-time weak solutions is obtained.
文摘This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.
文摘In this paper we discuss the existence of at least three solutions for a class of gradient mixed boundary value systems. The approach is fully based on a recent three critical points theorem of B. Ricceri [A three critical points theorem revisited, Nonlinear Anal., 70：9（2009）,3084-3089].
文摘In this paper, the relationship between the time dependent solutions and steady state solutions of the semiconductor equations affected by magnetic field is considered. A decay estimate is proved by a series of estimates on the solutions under some condition.
基金The work of the first author is supported in part by NSF of China No.11171227Research Fund for young teachers of Jiangsu Normal University No.11XLR27+3 种基金and Priority Academic Program Development of Jiangsu Higher Education Institutions.The work of the second author is supported in part by NSF of China No.11171227Fund for Doctoral Authority of China No.20123127110001Fund for Einstitute of Shanghai Universities No.E03004and Leading Academic Discipline Project of Shanghai Municipal Education Commission No.J50101.
文摘In this paper,we propose the Laguerre spectral method for high order problems with mixed inhomogeneous boundary conditions.It is also available for approximated solutions growing fast at infinity.The spectral accuracy is proved.Numerical results demonstrate its high effectiveness.
基金Supported by the National Natural Science Foundation of China(No.11371348)
文摘The unsteady flow of viscous incompressible shear-thinning non-Newtonian fluid with mixed bound- ary is investigated. The boundary condition on the outflow is the modified natural boundary condition, it con- tains the additional nonlinear term, which enables us to control the kinetic energy of the backward flow. The global existence of weak solution is proved. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.
文摘In this paper, we investigate a new pseudospectral method for mixed boundary value problems defined on quadrilaterals. We introduce a new Legendre-Gauss type interpolation and establish the basic approximation results, which play important roles in pseudospectral method for partial differential equations defined on quadrilaterals. We propose pseudospee- tral method for two model problems and prove their spectral accuracy. Numerical results demonstrate their high efficiency. The approximation results developed in this paper are also applicable to other problems defined on complex domains.
