By means of an equivalent invariant form of boundary conditions, the authors get the exis- tence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems...By means of an equivalent invariant form of boundary conditions, the authors get the exis- tence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with general nonlinear boundary conditions.展开更多
For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an appl...For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.展开更多
The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial data. By con...The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data.展开更多
In this paper, oscillatory properties for solutions of the systems of certain quasilinear impulsive delay hyperbolic equations with nonlinear diffusion coefficient are investigated. A sufficient criterion for oscillat...In this paper, oscillatory properties for solutions of the systems of certain quasilinear impulsive delay hyperbolic equations with nonlinear diffusion coefficient are investigated. A sufficient criterion for oscillations of such systems is obtained.展开更多
By means of the theory on the semi-global C^1 solution to the mixed initialboundary value problem （IBVP） for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomo...By means of the theory on the semi-global C^1 solution to the mixed initialboundary value problem （IBVP） for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomous first order quasilinear hyperbolic systems with general nonlinear boundary conditions.展开更多
The initial value problems and the first boundary problems for the quasilinear wave equation u_(tt)-[a_0+na_1(u_x)^(n-1)]u_(xx)-a_2u_(xxtt)=0 are considered,where a_0,a_2>0 are constants,a_1 is an arbitrary real nu...The initial value problems and the first boundary problems for the quasilinear wave equation u_(tt)-[a_0+na_1(u_x)^(n-1)]u_(xx)-a_2u_(xxtt)=0 are considered,where a_0,a_2>0 are constants,a_1 is an arbitrary real number,n is a natural number.The existence and uniqueness of the classical solutions for the initial value problems and the first boundary problems of the equation (1) are proved by the Galerkin method.展开更多
In this paper, the first boundary problem of quasilinear parabolic system of second order is studied by the finite difference method with intrinsic parallelism. for the problem, the stability of the difference schemes...In this paper, the first boundary problem of quasilinear parabolic system of second order is studied by the finite difference method with intrinsic parallelism. for the problem, the stability of the difference schemes with intrinsic parallelism are justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problem, without assuming the existence of the smooth solutions for the origillal problem.展开更多
In this paper,the authors define the strong (weak) exact boundary controllability and the strong (weak) exact boundary observability for first order quasilinear hyperbolic systems,and study their properties and the re...In this paper,the authors define the strong (weak) exact boundary controllability and the strong (weak) exact boundary observability for first order quasilinear hyperbolic systems,and study their properties and the relationship between them.展开更多
Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in a N-ball or an annulus without monotone assumptions on the nonlinear term f.It is also proved...Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in a N-ball or an annulus without monotone assumptions on the nonlinear term f.It is also proved that there is no non-radial positive solution.展开更多
The present paper investigates the asymptotic behavior of solutions for a class of second order inhomogeneous quasilinear equations on a three dimensional semiinfinite cylinder. A Phragmen-Lindelof type alternative is...The present paper investigates the asymptotic behavior of solutions for a class of second order inhomogeneous quasilinear equations on a three dimensional semiinfinite cylinder. A Phragmen-Lindelof type alternative is obtained, i.e., it is shown that in appropriate norms solutions of the equations either grow or decay as some spatial variable tends to infinity.展开更多
For a class of mixed initial-boundary value problem for general quasilinear hyperbolic sys-tems with zero eigenvalues, the authors establish the local exact controllability with boundary controls acting on one end or ...For a class of mixed initial-boundary value problem for general quasilinear hyperbolic sys-tems with zero eigenvalues, the authors establish the local exact controllability with boundary controls acting on one end or on two ends and internai controls acting on a part of equations in the system.展开更多
The authors consider the Cauchy problem with a kind of non-smooth initial data for quasilinear hyperbolic systems and obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global wea...The authors consider the Cauchy problem with a kind of non-smooth initial data for quasilinear hyperbolic systems and obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution.展开更多
A kind of the general finite difference schemes with intrinsic parallelism for the boundary value problem of the quasilinear parabolic system is studied without assuming heuristically that the original boundary value ...A kind of the general finite difference schemes with intrinsic parallelism for the boundary value problem of the quasilinear parabolic system is studied without assuming heuristically that the original boundary value problem has the unique smooth vector solution. By the method of a priori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixed-point technique in finite dimensional Euclidean space, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete W 2 (2,1) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original quasilinear parabolic problem is proved.展开更多
In this article, we study the quasilinear elliptic problem involving critical Hardy Sobolev exponents and Hardy terms. By variational methods and analytic techniques, we obtain the existence of sign-changing solutions...In this article, we study the quasilinear elliptic problem involving critical Hardy Sobolev exponents and Hardy terms. By variational methods and analytic techniques, we obtain the existence of sign-changing solutions to the problem.展开更多
基金the Special Funds for Major State Basic Research Projects of China.
文摘By means of an equivalent invariant form of boundary conditions, the authors get the exis- tence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with general nonlinear boundary conditions.
基金Project supported by the Special Funds forMajor State Basic Research Projects ofChina.
文摘For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.
基金Project supported by the National Natural Science Foundation of China
文摘The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data.
基金Supported by Hunan Provincial NSF(05jj400008)of China under Grant.
文摘In this paper, oscillatory properties for solutions of the systems of certain quasilinear impulsive delay hyperbolic equations with nonlinear diffusion coefficient are investigated. A sufficient criterion for oscillations of such systems is obtained.
基金Project supported by Specialized Research Fund for the Doctoral Program of Higher Education.
文摘By means of the theory on the semi-global C^1 solution to the mixed initialboundary value problem （IBVP） for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomous first order quasilinear hyperbolic systems with general nonlinear boundary conditions.
文摘The initial value problems and the first boundary problems for the quasilinear wave equation u_(tt)-[a_0+na_1(u_x)^(n-1)]u_(xx)-a_2u_(xxtt)=0 are considered,where a_0,a_2>0 are constants,a_1 is an arbitrary real number,n is a natural number.The existence and uniqueness of the classical solutions for the initial value problems and the first boundary problems of the equation (1) are proved by the Galerkin method.
文摘In this paper, the first boundary problem of quasilinear parabolic system of second order is studied by the finite difference method with intrinsic parallelism. for the problem, the stability of the difference schemes with intrinsic parallelism are justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problem, without assuming the existence of the smooth solutions for the origillal problem.
基金supported by the Basic Research Program of China(No. 2007CB814800)
文摘In this paper,the authors define the strong (weak) exact boundary controllability and the strong (weak) exact boundary observability for first order quasilinear hyperbolic systems,and study their properties and the relationship between them.
基金Supported by the Youth Foundations of National Education Commuttee the Committee on Science and Technology of Henan Province
文摘Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in a N-ball or an annulus without monotone assumptions on the nonlinear term f.It is also proved that there is no non-radial positive solution.
文摘The present paper investigates the asymptotic behavior of solutions for a class of second order inhomogeneous quasilinear equations on a three dimensional semiinfinite cylinder. A Phragmen-Lindelof type alternative is obtained, i.e., it is shown that in appropriate norms solutions of the equations either grow or decay as some spatial variable tends to infinity.
基金the Special Funds for Major State Basic Research Projects of China.
文摘For a class of mixed initial-boundary value problem for general quasilinear hyperbolic sys-tems with zero eigenvalues, the authors establish the local exact controllability with boundary controls acting on one end or on two ends and internai controls acting on a part of equations in the system.
基金Project supported by the Special Funds for Major State Basic Research Projects of China
文摘The authors consider the Cauchy problem with a kind of non-smooth initial data for quasilinear hyperbolic systems and obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution.
基金This work was supported by China“National Key Program for Developing Basic Sciences”G1999032801the National Natural Science Foundation of China(Grant No.19932010)the Foundation of CAEP(20020652).
文摘A kind of the general finite difference schemes with intrinsic parallelism for the boundary value problem of the quasilinear parabolic system is studied without assuming heuristically that the original boundary value problem has the unique smooth vector solution. By the method of a priori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixed-point technique in finite dimensional Euclidean space, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete W 2 (2,1) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original quasilinear parabolic problem is proved.
基金supported partly by the National Natural Science Foundation of China (10771219)
文摘In this article, we study the quasilinear elliptic problem involving critical Hardy Sobolev exponents and Hardy terms. By variational methods and analytic techniques, we obtain the existence of sign-changing solutions to the problem.
