标量守恒定律的哈密顿正则化

IF 1.1 3区数学 Q1 MATHEMATICS

Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI:10.3934/dcds.2023118

Billel Guelmame

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引用次数: 1

摘要

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。

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On a Hamiltonian regularization of scalar conservation laws

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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来源期刊

Discrete and Continuous Dynamical Systems 数学-数学

CiteScore

2.50

自引率

0.00%

发文量

175

审稿时长

6 months

期刊介绍： DCDS, series A includes peer-reviewed original papers and invited expository papers on the theory and methods of analysis, differential equations and dynamical systems. This journal is committed to recording important new results in its field and maintains the highest standards of innovation and quality. To be published in this journal, an original paper must be correct, new, nontrivial and of interest to a substantial number of readers.