Measure-valued solutions of scalar hyperbolic conservation laws, Part 1: Existence and time evolution of singular parts

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-24 DOI:10.1016/j.na.2024.113571

Michiel Bertsch , Flavia Smarrazzo , Andrea Terracina , Alberto Tesei

引用次数: 0

Abstract

We prove existence for a class of signed Radon measure-valued entropy solutions of the Cauchy problem for a first order scalar hyperbolic conservation law in one space dimension. The initial data of the problem is a finite superposition of Dirac masses, whereas the flux is Lipschitz continuous. Existence is proven by a constructive procedure which makes use of a suitable family of approximating problems. Relevant qualitative properties of such constructed solutions are pointed out.

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标量双曲守恒定律的量值解，第 1 部分：奇异部分的存在和时间演化

我们证明了一阶标量双曲守恒定律在一维空间中的考奇问题的一类有符号拉顿量值熵解的存在性。问题的初始数据是 Dirac 质量的有限叠加，而通量是 Lipschitz 连续的。利用合适的近似问题族的构造过程证明了问题的存在性。研究还指出了这种构造解的相关定性特性。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.