On weak stability of shock waves in 2D compressible elastodynamics

Standard

On weak stability of shock waves in 2D compressible elastodynamics. / Trakhinin, Yuri.

In: Journal of Hyperbolic Differential Equations, Vol. 19, No. 1, 01.03.2022, p. 157-173.

Research output: Contribution to journal › Article › peer-review

Harvard

Trakhinin, Y 2022, 'On weak stability of shock waves in 2D compressible elastodynamics', Journal of Hyperbolic Differential Equations, vol. 19, no. 1, pp. 157-173. https://doi.org/10.1142/S0219891622500035

APA

Trakhinin, Y. (2022). On weak stability of shock waves in 2D compressible elastodynamics. Journal of Hyperbolic Differential Equations, 19(1), 157-173. https://doi.org/10.1142/S0219891622500035

Vancouver

Trakhinin Y. On weak stability of shock waves in 2D compressible elastodynamics. Journal of Hyperbolic Differential Equations. 2022 Mar 1;19(1):157-173. doi: 10.1142/S0219891622500035

Author

Trakhinin, Yuri. / On weak stability of shock waves in 2D compressible elastodynamics. In: Journal of Hyperbolic Differential Equations. 2022 ; Vol. 19, No. 1. pp. 157-173.

BibTeX

@article{ba0f7edfd2ea44fb8918381d6ebb9d40,

title = "On weak stability of shock waves in 2D compressible elastodynamics",

abstract = "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.",

keywords = "Compressible elastodynamics, shock waves, weak stability, BOUNDARY-VALUE-PROBLEMS, VORTEX SHEETS, SYSTEMS",

author = "Yuri Trakhinin",

note = "This research was supported by the Russian Science Foundation under Grant No. 2011-20036. Publisher Copyright: {\textcopyright} 2022 World Scientific Publishing Co. Pte Ltd. All rights reserved.",

year = "2022",

month = mar,

day = "1",

doi = "10.1142/S0219891622500035",

language = "English",

volume = "19",

pages = "157--173",

journal = "Journal of Hyperbolic Differential Equations",

issn = "0219-8916",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

number = "1",

}

RIS

TY - JOUR

T1 - On weak stability of shock waves in 2D compressible elastodynamics

AU - Trakhinin, Yuri

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