Delta Shocks as Solutions of Conservation Laws with Discontinuous Moving Source

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-22 DOI:10.1007/s10884-023-10338-3

C. O. R. Sarrico

引用次数: 0

Abstract

A Riemann problem for the conservation law \(u_{t}+[\phi (u)]_{x}=kH(x-vt)\), where x, t, k, v and \(u=u(x,t)\) are real numbers, is studied with the goal of getting singular solutions in a convenient space of distributions that contains delta shock waves. Here \(\phi \) stands for an entire function taking real values on the real axis and H represents the Heaviside function. When u is seen as a density of matter some surprises may appear such as the creation of matter from a vacuum state. In a particular case, as the time goes on, such a matter grows continuously, running away from any spatial bounded region, what can be viewed as a unidimensional model of universe.

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三角冲击作为不连续移动源的守恒定律解

研究了守恒律 \(u_{t}+[\phi (u)]_{x}=kH(x-vt)\) 的黎曼问题，其中 x、t、k、v 和 \(u=u(x,t)\) 均为实数，目的是在包含三角冲击波的方便分布空间中得到奇异解。这里，\(\phi \)代表在实轴上取实值的全函数，H 代表海维塞德函数。当 u 被视为物质密度时，可能会出现一些令人惊讶的现象，例如从真空状态产生物质。在一种特殊情况下，随着时间的推移，这种物质会不断增长，远离任何空间边界区域，这可以看作是一种单维宇宙模型。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.