Sharp a-contraction estimates for small extremal shocks

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2023-09-01 DOI:10.1142/s0219891623500170

William Golding, Sam Krupa, Alexis Vasseur

引用次数: 4

Abstract

In this paper, we study the [Formula: see text]-contraction property of small extremal shocks for 1-d systems of hyperbolic conservation laws endowed with a single convex entropy, when subjected to large perturbations. We show that the weight coefficient [Formula: see text] can be chosen with amplitude proportional to the size of the shock. The main result of this paper is a key building block in the companion paper [G. Chen, S. G. Krupa and A. F. Vasseur, Uniqueness and weak-BV stability for [Formula: see text] conservation laws, Arch. Ration. Mech. Anal. 246(1) (2022) 299–332] in which uniqueness and BV-weak stability results for [Formula: see text] systems of hyperbolic conservation laws are proved.

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对小的极端冲击的急剧收缩估计

在本文中，我们研究了具有单一凸熵的双曲守恒律的一维系统在受到大扰动时的小极值激波的收缩性质。我们表明，权重系数[公式:见文]可以选择与冲击大小成比例的振幅。本文的主要结果是同伴论文[G.]中的关键组成部分。陈绍光、陈志强，守恒律的唯一性和弱bv稳定性[公式:见文本]，第3期。配给。动力机械。其中证明了双曲守恒律系统的唯一性和bv -弱稳定性结果[公式:见文本]。

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.