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 共查询到17条相似文献,搜索用时 62 毫秒
1.
高阶拟线性双曲型方程的精确边界能控性   总被引:1,自引:0,他引:1  
By means of the existence and uniqueness of semi-global C^1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigenvalues ,the local exact boundary controllability for higher order quasilinear hyperbolic equations is established.  相似文献   

2.
By means of the continuous Glimm functional,a proof is given on the global existence ofclassical solutions to Cauchy problem for general first order quasilinear hyperbolic systems withsmall initial total rariation.  相似文献   

3.
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   

4.
Lipschitz continuous solutions to the Cauchy problem for 1-D first order quasilinear hyperbolic systems are considered. Based on the methods of approximation and integral equations,the author gives two...  相似文献   

5.
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   

6.
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   

7.
In this article we prove that certain kinds of inhomogeneous terms can smoothen thesolution,for first order quasilinear hyperbolic systems globally in time provided that theinitial data are small.  相似文献   

8.
In this paper,the convergence of time-dependent Euler-Maxwell equations to compressible Euler-Poisson equations in a torus via the non-relativistic limit is studied. The local existence of smooth solutions to both systems is proved by using energy esti- mates for first order symmetrizable hyperbolic systems.For well prepared initial data the convergence of solutions is rigorously justified by an analysis of asymptotic expansions up to any order.The authors perform also an initial layer analysis for general initial data and prove the convergence of asymptotic expansions up to first order.  相似文献   

9.
In this paper the authors prove the existence and uniqueness of global classicalsolutions to the typical free boundary problem for general quasilinear hyperbolic systems.As an application,a unique global discontinuous solution only containing n shocks ont≥0 is obtained for a class of generalized Riemann problem for the quasilinear hyperbolicsystem of n conservation laws.  相似文献   

10.
It is wellknown that, for the Cauchy problem of quasilinear hyperbolic systems, in general, discontinuities may occur in solutions as the time variable increses, even if the initial data are sufficiently smooth. On the other hand, there exist some examples in which the solution of the corresponding Cauchy problem for quasilinear hyperbolic systems are globally smooth. Therefore, it is of great interest to determine the conditions under which solutions are globally smooth and the conditions under which singularities of the solution  相似文献   

11.
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   

12.
本文考察了弱线性退化的一阶非齐次拟线性严格双曲组具有小初值的柯西问题.在非齐次项满足匹配条件的假设下,给出了精细的波的分解公式,利用这些公式,证明了整体C1解的存在唯一性和稳定性.  相似文献   

13.
In this paper, we investigate initial value problems for hyperbolic mean curvature flow with a dissipative term. By means of support functions of a convex curve, a hyperbolic Monge-Amp`ere equation is derived, and this equation could be reduced to the first order quasilinear systems in Riemann invariants. Using the theory of the local solutions of Cauchy problems for quasilinear hyperbolic systems, we discuss lower bounds on life-span of classical solutions to Cauchy problems for dissipative hyperbolic mean curvature flow.  相似文献   

14.
该文给出了线性退化的严格双曲组具慢衰减及小全变差初值的Cauchy问题的经典解的整体存在唯一性. 这个结果进一步推广了A Bressan的相关结果  相似文献   

15.
高维拟线性双曲型方程组的对角化问题   总被引:1,自引:0,他引:1  
本文讨论了高维一阶拟线性方程组可对角化的条件,并给出其在二维等熵流方程组、三维空气动力学方程组及具有旋转对称性的守恒律组等情形的应用;然后给出了高维拟线性对角型方程组Cauchy问题存在整体经典解的一个充要条件,并给出其应用。  相似文献   

16.
In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {(t, x) | t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.  相似文献   

17.
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   

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