T5 Configurations and Hyperbolic Systems

IF 1.2 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics Pub Date : 2022-08-23 DOI:10.1142/S021919972250081X

Carl Johan Peter Johansson, Riccardo Tione

引用次数: 3

Abstract

In this paper we study the rank-one convex hull of a differential inclusion associated to entropy solutions of a hyperbolic system of conservation laws. This was introduced in Section 7 of [Kirchheim, M\"uller, \v{S}ver\'ak, 2003] and many of its properties have already been shown in [Lorent, Peng, 2019]-[Lorent, Peng, 2020]. In particular, in [Lorent, Peng 2020] it is shown that the differential inclusion does not contain any $T_4$ configurations. Here we continue that study by showing that the differential inclusion does not contain $T_5$ configurations.

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T5配置和双曲型系统

本文研究了与双曲守恒律系统熵解相关的微分包含的一阶凸包。这在[Kirchheim，M\“uller，\v{S}ver\'ak，2003]及其许多性质已经在[Rorent，Peng，2019]-[Rorent、Peng，2020]中展示。特别地，在[Rorent，Peng 2020]中，证明了微分包含不包含任何$T_4$配置。在这里，我们通过证明微分包含不包含$T_5$配置来继续这项研究。

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 Contemporary Mathematics 数学-数学

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： With traditional boundaries between various specialized fields of mathematics becoming less and less visible, Communications in Contemporary Mathematics (CCM) presents the forefront of research in the fields of: Algebra, Analysis, Applied Mathematics, Dynamical Systems, Geometry, Mathematical Physics, Number Theory, Partial Differential Equations and Topology, among others. It provides a forum to stimulate interactions between different areas. Both original research papers and expository articles will be published.