On weak stability of shock waves in 2D compressible elastodynamics

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

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.

Язык оригиналаанглийский
Страницы (с-по)157-173
Число страниц17
ЖурналJournal of Hyperbolic Differential Equations
Том19
Номер выпуска1
DOI
СостояниеОпубликовано - 1 мар. 2022

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