关于双曲型守恒律解的唯一性的评述

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2023-10-30 DOI:10.1007/s00205-023-01936-y

Alberto Bressan, Camillo De Lellis

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引用次数: 1

摘要

给定一个严格双曲\(n\times n\)守恒律系统，已知存在一个唯一的弱解Lipschitz半群，它被定义在一个总变分很小的函数域上，这是消失黏度近似的极限。本文的目的是证明在半群的域上，每一个取值的弱解，其激波满足Liu可容许条件，实际上与半群轨迹重合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A Remark on the Uniqueness of Solutions to Hyperbolic Conservation Laws

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A Remark on the Uniqueness of Solutions to Hyperbolic Conservation Laws

Given a strictly hyperbolic \(n\times n\) system of conservation laws, it is well known that there exists a unique Lipschitz semigroup of weak solutions, defined on a domain of functions with small total variation, which are limits of vanishing viscosity approximations. The aim of this note is to prove that every weak solution taking values in the domain of the semigroup, and whose shocks satisfy the Liu admissibility conditions, actually coincides with a semigroup trajectory.

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.