On a Hamiltonian regularization of scalar conservation laws

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/dcds.2023118

Billel Guelmame

引用次数: 1

Abstract

In this paper, we propose a Hamiltonian regularization of scalar conservation laws, which is parametrized by $ \ell>0 $ and conserves an $ H^1 $ energy. We prove the existence of global weak solutions for this regularization. Furthermore, we demonstrate that as $ \ell $ approaches zero, the unique entropy solution of the original scalar conservation law is recovered, providing justification for the regularization.This regularization belongs to a family of non-diffusive, non-dispersive regularizations that were initially developed for the shallow-water system and extended later to the Euler system. This paper represents a validation of this family of regularizations in the scalar case.

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标量守恒定律的哈密顿正则化

在本文中，我们提出了标量守恒律的哈密顿正则化，它被参数化为$ \ell>0 $，并且守恒$ H^1 $能量。我们证明了这种正则化的全局弱解的存在性。此外，我们证明了当$ \ well $趋于零时，原始标量守恒律的唯一熵解被恢复，为正则化提供了理由。这种正则化属于一种非扩散、非色散的正则化，最初是为浅水系统开发的，后来扩展到欧拉系统。本文在标量情况下对这类正则化进行了验证。

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.

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