Shock interactions for the Burgers-Hilbert equation

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2022-04-05 DOI:10.1080/03605302.2022.2084628

A. Bressan, S. Galtung, Katrin Grunert, K. Nguyen

引用次数: 0

Abstract

Abstract This paper provides an asymptotic description of a solution to the Burgers-Hilbert equation in a neighborhood of a point where two shocks interact. The solution is obtained as the sum of a function with H 2 regularity away from the shocks plus a corrector term having an asymptotic behavior like close to each shock. A key step in the analysis is the construction of piecewise smooth solutions with a single shock for a general class of initial data.

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汉堡-希尔伯特方程的激波相互作用

摘要本文给出了Burgers-Hilbert方程在两个激波相互作用点附近解的渐近描述。该解是由一个具有H2正则性的远离冲击的函数加上一个具有类似于接近每个冲击的渐近行为的校正器项的和得到的。分析中的一个关键步骤是为一类一般的初始数据构造具有单个冲击的分段光滑解。

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

Communications in Partial Differential Equations 数学-数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.