Wave-front tracking for a quasi-linear scalar conservation law with hysteresis

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-23 DOI:10.1016/j.jmaa.2024.128900

Fabio Bagagiolo, Stefan Moreti

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引用次数: 0

Abstract

In this article we deal with the Cauchy problem for the quasi-linear scalar conservation law

u_{t} + F {(u)}_{t} + u_{x} = 0,

where

F

is a specific hysteresis operator, namely the Play operator. Hysteresis models a rate-independent memory relationship between the input u and its output. Its presence in the partial differential equation gives a particular non-local feature to the latter allowing us to capture phenomena that may arise in some application fields. Riemann problems and the interactions between shock lines are studied and via the so-called Wave-Front Tracking method a solution to the Cauchy problem with bounded variation initial data is constructed. The solution found satisfies an entropy-like condition, making it the unique solution in the class of entropy admissible ones.

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带滞后的准线性标量守恒定律的波前跟踪

本文讨论准线性标量守恒定律ut+F(u)t+ux=0 的柯西问题，其中 F 是一个特定的滞后算子，即 Play 算子。滞后是指输入 u 与输出之间与速率无关的记忆关系。它在偏微分方程中的存在使偏微分方程具有特殊的非局部特征，使我们能够捕捉到某些应用领域可能出现的现象。我们对黎曼问题和冲击线之间的相互作用进行了研究，并通过所谓的波前跟踪方法，构建了具有有界变化初始数据的考奇问题解。找到的解满足类似熵的条件，使其成为熵可容许解类中的唯一解。

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.