This paper is concerned with the Riemann-Hilbert problems of degenerate hyperbolic system in two general domains, where the boundary curves are given by the parameter equations of the arc length s. We prove the existe...This paper is concerned with the Riemann-Hilbert problems of degenerate hyperbolic system in two general domains, where the boundary curves are given by the parameter equations of the arc length s. We prove the existence and uniqueness of solutions to the Riemann-Hilbert problems by conformal deformations. The corre-sponding representations of solutions to the problems are also presented.展开更多
This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and ...This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and the Leray-Schauder fixed point theorem.展开更多
In this Paper the Riemann--Hilbert boundary value problem for first orderquasilinear complex equations of mixed (elliptic- hyperbolic ) type is discussed. Firstly, therepresentation theorem is given, afterwards by usi...In this Paper the Riemann--Hilbert boundary value problem for first orderquasilinear complex equations of mixed (elliptic- hyperbolic ) type is discussed. Firstly, therepresentation theorem is given, afterwards by using the method of successive iterations,the existence and uniqueness of solutions for the above problem are proved. In [1], A.V.Bitsadze discussed the Tricomi problem for some linear mixed equation of second order,which can be derived from the results of the present paper.展开更多
A nonlinear perturbed conservative system is discussed. BY means of Hadamard's theorem. the existence and uniqueness of the solution of the continuous problem arc proved. When the equation is discreted on the unif...A nonlinear perturbed conservative system is discussed. BY means of Hadamard's theorem. the existence and uniqueness of the solution of the continuous problem arc proved. When the equation is discreted on the uniform meshes, it is proved that the corresponding discrete problem has a unique solution, Finally, the accuracy of the numerical solution is considered and a simple algorithm is provided for solving the nonlinear difference equation.展开更多
The object of this paper is to investigate the three-dimensional electro- magnetic scattering problems in a two-layered background medium. These problems have an important application in today＇s technology, such as t...The object of this paper is to investigate the three-dimensional electro- magnetic scattering problems in a two-layered background medium. These problems have an important application in today＇s technology, such as to detect objects that are buried in soil. Here, we model both the exterior impedance problem and the inhomogeneous medium problem in R3. We establish uniqueness and existence for the solution of the two scattering problems, respectively.展开更多
The initial-irregular oblique derivative boundary value problems for nonlinear and nondivergence parabolic systems of second order equations in multiply connected domains are dealt with where coefficients of systems o...The initial-irregular oblique derivative boundary value problems for nonlinear and nondivergence parabolic systems of second order equations in multiply connected domains are dealt with where coefficients of systems of equations are meaurable. The uniqueness theorem of solutions for the above problems and some a priori estimates of solutions for the problems are given. And by using the above estimates of solutions and the Leray-Schauder theorem, the existence of solutions of the initial-boundary value problems is proved. The results are generalizations of corresponding theorems in literature.展开更多
基金Supported by the NSF of Shandong Province (Y2008A31)
文摘This paper is concerned with the Riemann-Hilbert problems of degenerate hyperbolic system in two general domains, where the boundary curves are given by the parameter equations of the arc length s. We prove the existence and uniqueness of solutions to the Riemann-Hilbert problems by conformal deformations. The corre-sponding representations of solutions to the problems are also presented.
文摘This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and the Leray-Schauder fixed point theorem.
文摘In this Paper the Riemann--Hilbert boundary value problem for first orderquasilinear complex equations of mixed (elliptic- hyperbolic ) type is discussed. Firstly, therepresentation theorem is given, afterwards by using the method of successive iterations,the existence and uniqueness of solutions for the above problem are proved. In [1], A.V.Bitsadze discussed the Tricomi problem for some linear mixed equation of second order,which can be derived from the results of the present paper.
文摘A nonlinear perturbed conservative system is discussed. BY means of Hadamard's theorem. the existence and uniqueness of the solution of the continuous problem arc proved. When the equation is discreted on the uniform meshes, it is proved that the corresponding discrete problem has a unique solution, Finally, the accuracy of the numerical solution is considered and a simple algorithm is provided for solving the nonlinear difference equation.
基金The NSF (10801046) of Chinathe Heilongjiang Education Committee Grant(11551362,11551364)the Heilongjiang University Grant(Hdtd2010-14)
文摘The object of this paper is to investigate the three-dimensional electro- magnetic scattering problems in a two-layered background medium. These problems have an important application in today＇s technology, such as to detect objects that are buried in soil. Here, we model both the exterior impedance problem and the inhomogeneous medium problem in R3. We establish uniqueness and existence for the solution of the two scattering problems, respectively.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19671006).
文摘The initial-irregular oblique derivative boundary value problems for nonlinear and nondivergence parabolic systems of second order equations in multiply connected domains are dealt with where coefficients of systems of equations are meaurable. The uniqueness theorem of solutions for the above problems and some a priori estimates of solutions for the problems are given. And by using the above estimates of solutions and the Leray-Schauder theorem, the existence of solutions of the initial-boundary value problems is proved. The results are generalizations of corresponding theorems in literature.
文摘We prove an existence and uniqueness result for the Dirichlet problem for a class of elliptic equations with singular data in weighted Sobolev spaces.
