等温气体动力学的唯一性和弱bv稳定性

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-07-08 DOI:10.1016/j.jde.2025.113599

Jeffrey Cheng

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引用次数: 0

摘要

对于一维等温欧拉系统，我们考虑熵的BV解族可能有很大的，但有限的总变化。我们证明了这些解对于系统的一类弱解的大扰动是稳定的，这些弱解甚至可能不是BV。该方法基于一种改进的前沿跟踪算法的构建，其中以冲击的a-收缩与位移理论为构建块。主要贡献是在大bv环境下构造改进前跟踪算法的权值。

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Uniqueness & weak-BV stability in the large for isothermal gas dynamics

For the 1-d isothermal Euler system, we consider the family of entropic BV solutions with possibly large, but finite, total variation. We show that these solutions are stable with respect to large perturbations in a class of weak solutions to the system which may not even be BV. The method is based on the construction of a modified front tracking algorithm, in which the theory of a-contraction with shifts for shocks is used as a building block. The main contribution is to construct the weight in the modified front tracking algorithm in a large-BV setting.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics