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

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