Global piecewise classical solutions to quasilinear hyperbolic systems on a tree-like network

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2022-09-01 DOI:10.1142/s0219891622500151

Libin Wang, Ke Wang

引用次数: 0

Abstract

In this paper, we discuss the existence, uniqueness and asymptotic stability of global piecewise [Formula: see text] solution to the mixed initial-boundary value problem for 1-D quasilinear hyperbolic systems on a tree-like network. Under the assumption of boundary dissipation, when the given boundary and interface functions possess suitably small [Formula: see text] norm, we obtain the existence and uniqueness of global piecewise [Formula: see text] solution. Moreover, when they further possess a polynomial or exponential decaying property with respect to [Formula: see text], then the corresponding global piecewise [Formula: see text] solution possesses the same or similar decaying property. These results will be used to show the asymptotic stability of the exact boundary controllability of nodal profile on a tree-like network.

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树状网络上拟线性双曲型系统的全局分段经典解

本文讨论了一类树状网络上1-D拟线性双曲型系统混合初边值问题的整体分段解的存在唯一性和渐近稳定性。在边界耗散的假设下，当给定的边界和界面函数具有适当小的范数时，我们得到了全局分段解的存在唯一性。此外，当它们进一步对[公式:见文]具有多项式或指数衰减性质时，则相应的全局分段[公式:见文]解具有相同或类似的衰减性质。这些结果将用于证明树状网络上节点轮廓的精确边界可控性的渐近稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.