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On weak stability of shock waves in 2D compressible elastodynamics. / Trakhinin, Yuri.
в: Journal of Hyperbolic Differential Equations, Том 19, № 1, 01.03.2022, стр. 157-173.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On weak stability of shock waves in 2D compressible elastodynamics
AU - Trakhinin, Yuri
N1 - This research was supported by the Russian Science Foundation under Grant No. 2011-20036. Publisher Copyright: © 2022 World Scientific Publishing Co. Pte Ltd. All rights reserved.
PY - 2022/3/1
Y1 - 2022/3/1
N2 - By using an equivalent form of the uniform Lopatinski condition for 1-shocks, we prove that the stability condition found by the energy method in [A. Morando, Y. Trakhinin and P. Trebeschi, Structural stability of shock waves in 2D compressible elastodynamics, Math. Ann. 378 (2020) 1471-1504] for the rectilinear shock waves in two-dimensional flows of compressible isentropic inviscid elastic materials is not only sufficient but also necessary for uniform stability (implying structural nonlinear stability of corresponding curved shock waves). The key point of our spectral analysis is a delicate study of the transition between uniform and weak stability. Moreover, we prove that the rectilinear shock waves are never violently unstable, i.e. they are always either uniformly or weakly stable.
AB - By using an equivalent form of the uniform Lopatinski condition for 1-shocks, we prove that the stability condition found by the energy method in [A. Morando, Y. Trakhinin and P. Trebeschi, Structural stability of shock waves in 2D compressible elastodynamics, Math. Ann. 378 (2020) 1471-1504] for the rectilinear shock waves in two-dimensional flows of compressible isentropic inviscid elastic materials is not only sufficient but also necessary for uniform stability (implying structural nonlinear stability of corresponding curved shock waves). The key point of our spectral analysis is a delicate study of the transition between uniform and weak stability. Moreover, we prove that the rectilinear shock waves are never violently unstable, i.e. they are always either uniformly or weakly stable.
KW - Compressible elastodynamics
KW - shock waves
KW - weak stability
KW - BOUNDARY-VALUE-PROBLEMS
KW - VORTEX SHEETS
KW - SYSTEMS
UR - http://www.scopus.com/inward/record.url?scp=85128730486&partnerID=8YFLogxK
U2 - 10.1142/S0219891622500035
DO - 10.1142/S0219891622500035
M3 - Article
VL - 19
SP - 157
EP - 173
JO - Journal of Hyperbolic Differential Equations
JF - Journal of Hyperbolic Differential Equations
SN - 0219-8916
IS - 1
ER -
ID: 35894411