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1.
By means of the theory on the semi-global C1 solution to the mixed initial-boundary 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.  相似文献   

2.
Under the internal dissipative condition, the Cauchy problem for inhomogeneous quasilinear hyperbolic systems with small initial data admits a unique global C1 solution, which exponentially decays to zero as t → +∞, while if the coefficient matrixΘ of boundary conditions satisfies the boundary dissipative condition, the mixed initialboundary value problem with small initial data for quasilinear hyperbolic systems with nonlinear terms of at least second order admits a unique global C1 solution, which also exponentially decays to zero as t → +∞. In this paper, under more general conditions, the authors investigate the combined effect of the internal dissipative condition and the boundary dissipative condition, and prove the global existence and exponential decay of the C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with small initial data. This stability result is applied to a kind of models, and an example is given to show the possible exponential instability if the corresponding conditions are not satisfied.  相似文献   

3.
Sufficient conditions are obtained for the oscillation of solutions of the systems of quasilinear hyperbolic differential equation with deviating arguments under nonlinear boundary condition.  相似文献   

4.
Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local boundary(weak) observability for a coupled system of 1-D quasilinear wave equations with various types of boundary conditions.  相似文献   

5.
In this paper, the authors prove the global existence and uniqueness of classical solutions to some free boundary problems with characteristic boundary for the reducible quasilinear hyperbolic system.  相似文献   

6.
正Exact Boundary Observability for a Kind of Second-Order Quasilinear Hyperbolic Systems Ke WANG Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems,the local exact boundary observability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.  相似文献   

7.
In this paper,the author studies the global existence,singularities and life span of smooth solutions of the Cauchy problem for a class of quasilinear hyperbolic systems with higher order dissipative terms and gives their applications to nonlinear wave equations with higher order dissipative terms.  相似文献   

8.
The initial bounary value problem for quasilinear hyperbolic-parabolic coupled systemsin higher dimensional spaces,which arises in many mechanical problems is considered.Underthe assumptions that the hyperbolic part of the coupled system is a quasilinear symmetrichyperbolic system and the parabolic part is a quasilinear parabolic system of second orderand suitble asstunptions of smoothness and compatibiliy conditions,the existence anduniqueness of local smooth solution is proved in the cases that the boundary of domain isnoncharacteristic or uniformly characteristic with respect to the hyperbolic part.As an application,the existence and uniqueness of local smooth solution for the initialboundary problem of the radiation hydrodynamic system,as well as of the viscous compressiblehydrodynamic system,with solid wall boundary,is obtained.  相似文献   

9.
BREAKDOWN OF CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS   总被引:1,自引:0,他引:1  
This paper deals with the asymptotic behavior of the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with weaker decaying initial data, and obtains a blow-up result for C1 solution to Cauchy problem.  相似文献   

10.
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.  相似文献   

11.
In this paper, by means of a constructive method based on the existence and uniqueness of the semi-global C2 solution, we establish the local exact boundary observability for a kind of second order quasilinear hyperbolic systems. As an application, we obtain the one-sided local exact boundary observability for a kind of first order quasilinear hyperbolic systems of diagonal form with boundary conditions in which the diagonal variables corresponding to the positive eigenvalues and those corresponding to the negative eigenvalues are decoupled.  相似文献   

12.
In this paper, by means of a constructive method based on the existence and uniqueness of the semi‐global C2 solution, we establish the local exact boundary controllability for a kind of second‐order quasilinear hyperbolic systems. As an application, we obtain the one‐sided local exact boundary controllability for the first‐order quasilinear hyperbolic systems of diagonal form with boundary conditions in which the diagonal variables corresponding to the positive eigenvalues and those corresponding to the negative eigenvalues are decoupled. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

13.
The initial bounary value problem for quasilinear byperbolie-parabolic coupled systems in higher dimensional spaces, which arises in many mechanical problerns is considered. Under the assumptions that the-hyperbolic part of the coupled system is a quasilinear symmetric hyperbolic system and the parabolic part is a quasilinear parabolic system of second order and suitable assumptions of smoothness and compatibiliy conditions, the existence and uniqueness of local smooth solution is proved in the cases that the boundary of domain is noncharacteristic or uniformly characteristic with respect to the hyperbolic part. As an application, the existence and uniqueness of local smooth solution for the initial boundary problem of the radiation hydrodynamic system, as well as of the viscous compressible hydrodynamic system, with solid wal1 boundary, is obtained.  相似文献   

14.
In this paper, the synchronization for a kind of first order quasilinear hyperbolic system is taken into account. In this system, all the equations share the same positive wave speed. To realize the synchronization, a uniform constructive method is adopted, rather than an iteration process usually used in dealing with nonlinear systems. Furthermore, similar results on the exact boundary synchronization by groups can be obtained for a kind of first order quasilinear hyperbolic system of equations with different positive wave speeds by groups.  相似文献   

15.
利用一阶拟线性双曲组混合初边值问题的精确能控性理论,通过对边界速度或压强的控制,实现了一维绝热流方程组的精确边界能控性.  相似文献   

16.
在可交换四元数空间中的双曲方程的特征边值问题   总被引:1,自引:0,他引:1  
杨丕文  李曼荔  杨硕 《数学学报》2007,50(6):1249-125
讨论了一阶和二阶双曲复方程的特征边值问题.对其中两种线性方程,分别在不同的情况下获得通解和可解条件.而对于拟线性的二阶双曲复方程,证明了解的存在性和唯一性.  相似文献   

17.
本文证明了具零特征且形式更广泛的一类拟线性双曲型方程组的具有一般非线性边界条件的混合初 一边值问题半整体C1解的存在唯一性.  相似文献   

18.
Numerical approximations of Cahn-Hilliard phase-field model for the two-phase incompressible flows are considered in this paper.Several efficient and energy stable time discretization schemes for the coupled nonlinear Cahn-Hilliard phase-field system for both the matched density case and the variable density case are constructed,and are shown to satisfy discrete energy laws which are analogous to the continuous energy laws.  相似文献   

19.
Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the local exact boundary observability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.  相似文献   

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