共查询到20条相似文献,搜索用时 18 毫秒
1.
In this paper, we consider the class of so-called weakly hyperbolic linear systems, which includes correct and hyperbolic (exponentially-dichotomous) systems. We prove new results generalizing related classical theorems on the conditional stability of solutions. We establish the existence of stable manifolds consisting of points corresponding to the solutions of such systems with negative Lyapunov exponents. We study the behavior of solutions starting outside the stable manifold. The technique used in our paper is similar to that in the theory of hyperbolic systems. 相似文献
2.
A. E. Alekseenko A. S. Kholodov Ya. A. Kholodov 《Computational Mathematics and Mathematical Physics》2016,56(6):916-931
For quasilinear systems of hyperbolic equations, the nonclassical boundary value problem of controlling solutions with the help of boundary conditions is considered. Previously, this problem was extensively studied in the case of the simplest hyperbolic equations, namely, the scalar wave equation and certain linear systems. The corresponding problem formulations and numerical solution algorithms are extended to nonlinear (quasilinear and conservative) systems of hyperbolic equations. Some numerical (grid-characteristic) methods are considered that were previously used to solve the above problems. They include explicit and implicit conservative difference schemes on compact stencils that are linearizations of Godunov’s method. The numerical algorithms and methods are tested as applied to well-known linear examples. 相似文献
3.
Exact Controllability for Nonautonomous First Order Quasilinear Hyperbolic Systems 总被引:2,自引:0,他引:2
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Zhiqiang WANG 《数学年刊B辑(英文版)》2006,27(6):643-656
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
4.
Shuxing Chen 《Frontiers of Mathematics in China》2007,2(1):87-102
This paper is devoted to initial boundary value problems for quasi-linear symmetric hyperbolic systems in a domain with characteristic
boundary. It extends the theory on linear symmetric hyperbolic systems established by Friedrichs to the nonlinear case. The
concept on regular characteristics and dissipative boundary conditions are given for quasilinear hyperbolic systems. Under
some assumptions, an existence theorem for such initial boundary value problems is obtained. The theorem can also be applied
to the Euler system of compressible flow.
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Translated from Chinese Annals of Mathematics, Ser. A, 1982, 3(2): 223–232 相似文献
5.
Jacky Cresson 《Journal of Differential Equations》2003,187(2):269-292
We consider hyperbolic tori of three degrees of freedom initially hyperbolic Hamiltonian systems. We prove that if the stable and unstable manifold of a hyperbolic torus intersect transversaly, then there exists a hyperbolic invariant set near a homoclinic orbit on which the dynamics is conjugated to a Bernoulli shift. The proof is based on a new geometrico-dynamical feature of partially hyperbolic systems, the transversality-torsion phenomenon, which produces complete hyperbolicity from partial hyperbolicity. We deduce the existence of infinitely many hyperbolic periodic orbits near the given torus. The relevance of these results for the instability of near-integrable Hamiltonian systems is then discussed. For a given transition chain, we construct chain of hyperbolic periodic orbits. Then we easily prove the existence of periodic orbits of arbitrarily high period close to such chain using standard results on hyperbolic sets. 相似文献
6.
José F. Alves Ví tor Araú jo Benoî t Saussol 《Proceedings of the American Mathematical Society》2003,131(4):1303-1309
We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonuniformly expanding on sets of total probability (probability one with respect to every invariant probability measure) are necessarily uniformly expanding. We also present a version of this result for diffeomorphisms with nonuniformly hyperbolic sets.
7.
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
8.
Generalized Glimm scheme to the initial boundary value problem of hyperbolic systems of balance laws
John M. Hong 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):635-650
In this paper we provide a generalized version of the Glimm scheme to establish the global existence of weak solutions to the initial-boundary value problem of 2×2 hyperbolic systems of conservation laws with source terms. We extend the methods in [J.B. Goodman, Initial boundary value problem for hyperbolic systems of conservation laws, Ph.D. Dissertation, Stanford University, 1982; J.M. Hong, An extension of Glimm’s method to inhomogeneous strictly hyperbolic systems of conservation laws by “weaker than weak” solutions of the Riemann problem, J. Differential Equations 222 (2006) 515-549] to construct the approximate solutions of Riemann and boundary Riemann problems, which can be adopted as the building block of approximate solutions for our initial-boundary value problem. By extending the results in [J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965) 697-715] and showing the weak convergence of residuals, we obtain stability and consistency of the scheme. 相似文献
9.
3维双曲空间中曲面的双曲Gauss映照和法Gauss映照 总被引:3,自引:0,他引:3
本文导出了3维双曲空间中曲面的双曲Gauss映照和法Gauss映照的关系,发现了一般的曲面由双曲Gauss映照和平均曲率函数唯一确定,并证明了双曲Gauss映照所满足的二阶线性椭圆方程,给出了两种形式的关于双曲Gauss映照的三阶非线性偏微分方程(组)的一个解. 相似文献
10.
We study optimal control problems for hyperbolic equations
(focusing on the multidimensional wave equation) with control functions in the Dirichlet
boundary conditions under hard/pointwise control and state constraints. Imposing
appropriate convexity assumptions on the cost integral functional, we establish the
existence of optimal control and derive new necessary optimality conditions in the
integral form of the Pontryagin Maximum Principle for hyperbolic state-constrained systems. 相似文献
11.
Ke WANG 《数学年刊B辑(英文版)》2016,37(6):803-820
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
12.
In this article, first, the authors prove that there exists a unique global smooth solution for the Cauthy problem to the hyperbolic conservation laws systems with relaxation; second, in the large time station, they prove that the global smooth solutions of the hyperbolic conservation laws systems with relaxation converge to rarefaction waves solution at a determined L^P(p ≥ 2) decay rate. 相似文献
13.
S. P. Kuznetsov V. P. Kruglov 《Proceedings of the Steklov Institute of Mathematics》2017,297(1):208-234
Examples of mechanical systems with hyperbolic chaos are discussed, including the Thurston–Weeks–Hunt–MacKay hinge mechanism, in which conservative Anosov dynamics is realized, and dissipative systems with Smale–Williams type attractors (a particle on a plane under periodic kicks, interacting particles sliding on two alternately rotating disks, and a string with parametric excitation by modulated pump). The examples considered in the paper are interesting from the viewpoint of filling hyperbolic theory, as a well-developed field of the mathematical theory of dynamical systems, with physical content. The results of computer tests for hyperbolicity of the systems are presented that are based on the analysis of the statistics of intersection angles of stable and unstable manifolds. 相似文献
14.
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
15.
Lei YU 《数学年刊B辑(英文版)》2018,39(6):947-962
This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes the results in [Li, T. and Yu, L., One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws, To appear in Journal de Mathématiques Pures et Appliquées, 2016.] for a class of strictly hyperbolic systems of conservation laws. 相似文献
16.
By means of the theory on the semiglobal C1 solution to the mixed initial-boundary value problem for first-order quasilinear hyperbolic systems, we establish the local exact boundary observability for general nonautonomous first-order quasilinear hyperbolic systems without zero eigenvalues and reveal the essential difference between nonautonomous hyperbolic systems and autonomous hyperbolic systems. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
17.
Ya. Pesin 《Regular and Chaotic Dynamics》2007,12(5):476-489
This is a survey-type article whose goal is to review some recent results on existence of hyperbolic dynamical systems with
discrete time on compact smooth manifolds and on coexistence of hyperbolic and non-hyperbolic behavior. It also discusses
two approaches to the study of genericity of systems with nonzero Lyapunov exponents.
相似文献
18.
Yun-guang Lu 《Journal of Mathematical Analysis and Applications》2006,324(2):1407-1416
In this paper, a zero factor idea is introduced to extend the convergence framework in [G.-Q. Chen, C.D. Levermore, T.-P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math. 47 (1994) 787-830] for the singular limits of stiff relaxation from general 2×2 hyperbolic conservation systems to nonstrictly hyperbolic systems and an application of this framework on the so-called system of extended traffic flow is obtained. 相似文献
19.
Mapundi Banda Mohammed Seaïd 《Numerical Methods for Partial Differential Equations》2007,23(5):1211-1234
We present a class of high‐order weighted essentially nonoscillatory (WENO) reconstructions based on relaxation approximation of hyperbolic systems of conservation laws. The main advantage of combining the WENO schemes with relaxation approximation is the fact that the presented schemes avoid solution of the Riemann problems due to the relaxation approach and high‐resolution is obtained by applying the WENO approach. The emphasis is on a fifth‐order scheme and its performance for solving a wide class of systems of conservation laws. To show the effectiveness of these methods, we present numerical results for different test problems on multidimensional hyperbolic systems of conservation laws. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
20.
E. A. Gasymov 《Computational Mathematics and Mathematical Physics》2014,54(7):1144-1158
A mixed problem of matching in hyperbolic systems of different orders with irregular boundary conditions is considered. In particular, these systems include hyperbolic systems with coefficients having discontinuities of the first kind. Under certain conditions, an analytical representation of the solution of the problem is obtained by means of a finite integral transform. 相似文献