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On existence of shock waves in compressible neo-Hookean elastic materials. / Trakhinin, Yu L.

в: Theoretical and Mathematical Physics(Russian Federation), Том 225, № 1, 27.10.2025, стр. 1756-1772.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Trakhinin, YL 2025, 'On existence of shock waves in compressible neo-Hookean elastic materials', Theoretical and Mathematical Physics(Russian Federation), Том. 225, № 1, стр. 1756-1772. https://doi.org/10.1134/S0040577925100058

APA

Trakhinin, Y. L. (2025). On existence of shock waves in compressible neo-Hookean elastic materials. Theoretical and Mathematical Physics(Russian Federation), 225(1), 1756-1772. https://doi.org/10.1134/S0040577925100058

Vancouver

Trakhinin YL. On existence of shock waves in compressible neo-Hookean elastic materials. Theoretical and Mathematical Physics(Russian Federation). 2025 окт. 27;225(1):1756-1772. doi: 10.1134/S0040577925100058

Author

Trakhinin, Yu L. / On existence of shock waves in compressible neo-Hookean elastic materials. в: Theoretical and Mathematical Physics(Russian Federation). 2025 ; Том 225, № 1. стр. 1756-1772.

BibTeX

@article{b1ae40ae71f54e7b9d956471ec9c8047,
title = "On existence of shock waves in compressible neo-Hookean elastic materials",
abstract = "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.",
keywords = "compressible elastodynamics, local-in-time well-posedness of the free boundary problem, shock waves, uniform and weak Lopatinski conditions",
author = "Trakhinin, {Yu L.}",
note = "This research was supported by the Russian Science Foundation under grant No. 24-21-00192, https://rscf.ru/en/project/24-21-00192/. ",
year = "2025",
month = oct,
day = "27",
doi = "10.1134/S0040577925100058",
language = "English",
volume = "225",
pages = "1756--1772",
journal = "Theoretical and Mathematical Physics(Russian Federation)",
issn = "0040-5779",
publisher = "Springer Singapore",
number = "1",

}

RIS

TY - JOUR

T1 - On existence of shock waves in compressible neo-Hookean elastic materials

AU - Trakhinin, Yu L.

N1 - This research was supported by the Russian Science Foundation under grant No. 24-21-00192, https://rscf.ru/en/project/24-21-00192/.

PY - 2025/10/27

Y1 - 2025/10/27

N2 - 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.

AB - 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.

KW - compressible elastodynamics

KW - local-in-time well-posedness of the free boundary problem

KW - shock waves

KW - uniform and weak Lopatinski conditions

UR - https://www.mendeley.com/catalogue/b43e6db1-9ed2-31c2-bd19-ae64b031977a/

U2 - 10.1134/S0040577925100058

DO - 10.1134/S0040577925100058

M3 - Article

VL - 225

SP - 1756

EP - 1772

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

SN - 0040-5779

IS - 1

ER -

ID: 71580944