Multiple Riemann wave solutions of the general form of quasilinear hyperbolic systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-03-28 DOI:10.57262/ade028-0102-73

A. Grundland, J. Lucas

引用次数: 1

Abstract

. The objective of this paper is to construct geometrically Riemann k -wave solutions of the general form of ﬁrst-order quasilinear hyperbolic systems of partial diﬀerential equations. To this end, we adapt and combine elements of two approaches to the construction of Riemann k -waves, namely the symmetry reduction method and the generalized method of characteristics. We formulate a geometrical setting for the general form of the k -wave problem and discuss in detail the conditions for the existence of k -wave solutions. An auxiliary result concerning the Frobenius theorem is established. We use it to obtain formulae describing the k -wave solutions in closed form. Our theoretical considerations are illustrated by examples of hydrodynamic type systems including the Brownian motion equation.

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拟线性双曲型系统一般形式的多重黎曼波解

本文的目的是构造一阶拟线性双曲型偏微分方程组的一般形式的几何黎曼k波解。为此，我们采用并结合了两种构造黎曼k波的方法的元素，即对称约简方法和广义特征方法。我们为k波问题的一般形式建立了一个几何设置，并详细讨论了k波解存在的条件。建立了Frobenius定理的一个辅助结果。我们用它得到了描述封闭形式k波解的公式，并用包括布朗运动方程在内的流体动力学型系统的例子说明了我们的理论考虑。

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.