Abstract: We study the three-dimensional structural stability of shock waves for the equations of elastodynamics governing isentropic flows of compressible inviscid elastic materials. By nonlinear structural stability of a shock wave we mean the local-in-time existence and uniqueness of the discontinuous shock front solution to the hyperbolic system of elastodynamics. By using equivalent formulations of the uniform and weak Kreiss–Lopatinski conditions for 1-shocks, we show that planar shock waves in three-dimensional elastodynamics are always at least weakly stable, and we find a condition necessary and sufficient for their uniform stability. Since the system of elastodynamics satisfies the Agranovich–Majda–Osher block structure condition, uniform stability implies structural stability of corresponding nonplanar shock waves. We also show that, as in isentropic gas dynamics, all compressive shock waves are uniformly stable for convex equations of state. This paper is a natural continuation of the previous two-dimensional analysis in [25,31]. As in the two-dimensional case, we make the conclusion that the elastic force plays stabilizing role for uniform stability.

Cite: Shafeev A. , Trakhinin Y.
Three-dimensional structural stability of shock waves in elastodynamics
Zeitschrift fur Angewandte Mathematik und Physik. 2025. V.76. N5. 188 :1-18. DOI: 10.1007/s00033-025-02569-9 WOS Scopus OpenAlex

Dates:

Submitted:	May 24, 2025
Accepted:	Jul 29, 2025
Published print:	Aug 24, 2025
Published online:	Aug 24, 2025

Identifiers:

Web of science:	WOS:001558148200001
Scopus:	2-s2.0-105013839596
OpenAlex:	W4413478042

Citing: Пока нет цитирований

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