Following the pointwise semigroup approach of [ZH, MZ.1], we establish sharp pointwise Green function bounds and consequent linearized stability for viscous shock profiles of general hyperbolic-parabolic systems of conservation laws of dissipative type, under the necessary assumptions ([Z.1, Z.3, Z.4]) of spectral stability, i.e., stable point spectrum of the linearized operator about the wave; transversality of the connecting profile; and hyperbolic stability of the corresponding ideal shock of the associated inviscid system, with no additional assumptions on the structure or strength of the shock. These bounds are used in a companion paper [MZ.2] to establish nonlinear stability of small-amplitude Lax shocks of symmetrizable hyperbolic-parabolic systems.

Pointwise Green function bounds for shock profiles of systems with real viscosity / Mascia, Corrado; Kevin, Zumbrun. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 169:3(2003), pp. 177-263. [10.1007/s00205-003-0258-5]

Pointwise Green function bounds for shock profiles of systems with real viscosity

MASCIA, Corrado;
2003

Abstract

Following the pointwise semigroup approach of [ZH, MZ.1], we establish sharp pointwise Green function bounds and consequent linearized stability for viscous shock profiles of general hyperbolic-parabolic systems of conservation laws of dissipative type, under the necessary assumptions ([Z.1, Z.3, Z.4]) of spectral stability, i.e., stable point spectrum of the linearized operator about the wave; transversality of the connecting profile; and hyperbolic stability of the corresponding ideal shock of the associated inviscid system, with no additional assumptions on the structure or strength of the shock. These bounds are used in a companion paper [MZ.2] to establish nonlinear stability of small-amplitude Lax shocks of symmetrizable hyperbolic-parabolic systems.
2003
conservation laws; hyperbolic-parabolic systems; nonlinear stability; traveling waves
01 Pubblicazione su rivista::01a Articolo in rivista
Pointwise Green function bounds for shock profiles of systems with real viscosity / Mascia, Corrado; Kevin, Zumbrun. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 169:3(2003), pp. 177-263. [10.1007/s00205-003-0258-5]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/46529
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