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On existence of shock waves in compressible neo-Hookean elastic materials Full article

Journal Theoretical and Mathematical Physics (Russian Federation)
ISSN: 0040-5779 , E-ISSN: 1573-9333
Output data Year: 2025, Volume: 225, Number: 1, Pages: 1756-1772 Pages count : 17 DOI: 10.1134/S0040577925100058
Tags compressible elastodynamicsshock wavesuniform and weak Lopatinski conditionslocal-in-time well-posedness of the free boundary problem
Authors Trakhinin Yu.L. 1,2
Affiliations
1 Novosibirsk State University, Novosibirsk, Russia
2 Sobolev Institute of Mathematics, Novosibirsk, Russia

Funding (1)

1 Russian Science Foundation 24-21-00192

Abstract: We survey results on the structural stability of shock waves in elastodynamics of compressible neo-Hookean materials. By nonlinear structural stability of a shock wave we mean the local-in-time existence and uniqueness of the discontinuous shock front solution of the elastodynamics equations, which guarantees the real existence of the shock wave as a physical structure. We describe finding structural stability conditions for shock waves in 2D elastodynamics using both the energy method and spectral analysis of the corresponding linearized free boundary problem. We also briefly discuss recent results on structural stability in the general 3D case.
Cite: Trakhinin Y.L.
On existence of shock waves in compressible neo-Hookean elastic materials
Theoretical and Mathematical Physics (Russian Federation). 2025. V.225. N1. P.1756-1772. DOI: 10.1134/S0040577925100058 WOS Scopus
Original: Trakhinin Y.L.
О существовании ударных волн в сжимаемых неогуковских упругих материалах
Теоретическая и математическая физика. 2025. Т.225. №1. С.75-94. DOI: 10.4213/tmf10966 РИНЦ OpenAlex
Dates:
Submitted: Mar 3, 2025
Accepted: Apr 7, 2025
Published online: Oct 27, 2025
Published print: Nov 4, 2025
Identifiers:
Web of science: WOS:001603307100003
Scopus: 2-s2.0-105019757992
Citing: Пока нет цитирований
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