Nonuniqueness of a Self-similar Solution to the Riemann Problem for Elastic Waves in Media with a Negative Nonlinearity Parameter

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-12-20 DOI:10.1134/s008154382304020x

A. P. Chugainova, R. R. Polekhina

引用次数: 0

Abstract

We study self-similar solutions of the Riemann problem in the nonuniqueness region for weakly anisotropic elastic media with a negative nonlinearity parameter. We show that all discontinuities contained in the solutions in the nonuniqueness region have a stationary structure. We also show that in the nonuniqueness region one can construct two types of self-similar solutions.

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负非线性参数介质中弹性波的黎曼问题自相似解的非唯一性

摘要我们研究了具有负非线性参数的弱各向异性弹性介质的黎曼问题在非唯一性区域的自相似解。我们证明，非唯一性区域的解中包含的所有不连续性都具有静止结构。我们还证明，在非唯一性区域，可以构造两种自相似解。

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

Proceedings of the Steklov Institute of Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic.