Higher Regularity for Entropy Solutions of Conservation Laws with Geometrically Constrained Discontinuous Flux

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-04 DOI:10.1137/23m1604199

S. S. Ghoshal, S. Junca, A. Parmar

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 6121-6136, October 2024.
Abstract. For the Burgers’ equation, the entropy solution becomes instantly [math] with only [math] initial data. For conservation laws with genuinely nonlinear discontinuous flux, it is well known that the [math] regularity of entropy solutions is lost. Recently, this regularity has been proved to be fractional with [math]. Moreover, for less nonlinear flux, the solution still has a fractional regularity [math]. The resulting general rule is that the regularity of entropy solutions for a discontinuous flux is less than for a smooth flux. In this paper, an optimal geometric condition on the discontinuous flux is used to recover the same regularity as for the smooth flux with the same kind of nonlinearity.

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具有几何约束不连续通量的守恒定律熵解的较高正则性

SIAM 数学分析期刊》，第 56 卷第 5 期，第 6121-6136 页，2024 年 10 月。摘要对于布尔格斯方程，只需[数学]初始数据，熵解就会立即变成[数学]。众所周知，对于具有真正非线性不连续通量的守恒定律，熵解的[数学]正则性会丧失。最近，这种正则性被证明是分数[数学]的。此外，对于较小的非线性通量，解仍然具有分数正则性[math]。由此得出的一般规律是，非连续通量的熵解的正则性小于光滑通量的熵解的正则性。本文利用非连续通量的最优几何条件来恢复与具有同类非线性的光滑通量相同的正则性。

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

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.