Admissibility of discontinuities in the solutions of a hyperbolic 2 × 2 system of conservation laws

IF 2.8 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics Pub Date : 2025-06-11 DOI:10.1016/j.ijnonlinmec.2025.105174

A.P. Chugainova, R.R. Polekhina

引用次数: 0

Abstract

The problem of admissibility of discontinuities in the solutions of a hyperbolic system of two conservation laws describing quasitransverse waves in nonlinearly elastic weakly anisotropic media is studied. The standard viscous regularization method is applied to the defining system of equations. Regularization leads to the situation where two different viscosity profiles may correspond to the discontinuity. The analysis of the linear (spectral) stability of these two profiles has shown that one of them is stable while the other is unstable. This conclusion demonstrates that the definition of admissibility of a discontinuity should include the requirement of stability of the discontinuity structure (the viscosity profile).

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双曲2x2守恒律系统解中不连续的可容许性

研究了非线性弹性弱各向异性介质中描述准横波的两个守恒定律双曲系统解的不连续容许性问题。将标准粘性正则化方法应用于方程组的定义。正则化导致两种不同的粘度分布可能对应于不连续。对这两种剖面的线性（谱）稳定性分析表明，其中一种是稳定的，而另一种是不稳定的。这一结论表明，不连续结构容许性的定义应包括对不连续结构（粘度剖面）稳定性的要求。

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

International Journal of Non-Linear Mechanics 物理-力学

CiteScore

5.50

自引率

9.40%

发文量

192

审稿时长

67 days

期刊介绍： The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.