Differential and Integral Equations

Nonlinear stability of degenerate shock profiles

Peter Howard

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We consider degenerate viscous shock profiles arising in systems of two regularized conservation laws, where degeneracy here describes viscous shock profiles for which the asymptotic endstates are sonic to the associated hyperbolic system (the shock speed is equal to one of the characteristic speeds). Proceeding with pointwise estimates on the Green's function for the linear system of equations that arises upon linearization of the conservation law about a degenerate viscous shock profile, we establish that spectral stability, defined in terms of an Evans function, implies nonlinear stability. The asymptotic rate of decay for the perturbation is found both pointwise and in all $L^p$ norms, $p \ge 1$.

Article information

Source
Differential Integral Equations Volume 20, Number 5 (2007), 515-560.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039442

Mathematical Reviews number (MathSciNet)
MR2324219

Zentralblatt MATH identifier
1212.35298

Subjects
Primary: 35L65: Conservation laws
Secondary: 35B35: Stability 35B40: Asymptotic behavior of solutions 35K55: Nonlinear parabolic equations 35L67: Shocks and singularities [See also 58Kxx, 76L05]

Citation

Howard, Peter. Nonlinear stability of degenerate shock profiles. Differential Integral Equations 20 (2007), no. 5, 515--560. https://projecteuclid.org/euclid.die/1356039442.


Export citation