An 𝐿^{𝑝} shock admissibility condition for conservation laws

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2022-02-01 DOI:10.1090/qam/1610

Hiroki Ohwa

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引用次数: 1

Abstract

We estimate the L p L^p ( p > 0 p>0 ) local distance between piecewise constant solutions to the Cauchy problem of conservation laws and propose a shock admissibility condition for having an L p L^p local contraction of such solutions. Moreover, as an application, we prove that there exist L p L^p locally contractive solutions on some set of initial functions, to the Cauchy problem of conservation laws with convex or concave flux functions. As a result, for conservation laws with convex or concave flux functions, we see that rarefaction waves have an L q L^q ( q ≥ 1 q\geq 1 ) local contraction and shock waves have an L r L^r ( 0 > r ≤ 1 0>r\leq 1 ) local contraction.

查看原文本刊更多论文

一𝐿^{𝑝} 守恒定律的冲击可容许条件

我们估计了柯西守恒问题的分段常数解之间的lpl L^p (p>0 p>0)局部距离，并提出了这种解具有lpl L^p局部收缩的激波容许性条件。此外，作为一个应用，我们证明了具有凸或凹通量函数的柯西守恒律问题在一些初始函数集上存在L p L^p局部收缩解。因此，对于具有凸或凹通量函数的守恒律，我们看到，稀疏波具有lq L^q (q≥1q \geq 1)局部收缩，激波具有lr L^r (0>r≤10 >r \leq 1)局部收缩。

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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.