Long-time behavior of scalar viscous shock fronts in two dimensions

Jonathan Goodman, Judith R. Miller

Research output: Contribution to journalArticle

Abstract

We prove nonlinear stability in L1 of planar shock front solutions to a viscous conservation law in two spatial dimensions and obtain an expression for the asymptotic form of small perturbations. The leading-order behavior is shown rigorously to be governed by an effective diffusion coefficient depending on forces transverse to the shock front. The proof is based on a spectral analysis of the linearized problem.

Original languageEnglish (US)
Pages (from-to)255-277
Number of pages23
JournalJournal of Dynamics and Differential Equations
Volume11
Issue number2
StatePublished - 1999

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Long-time Behavior
Shock
Two Dimensions
Scalar
Viscous Conservation Laws
Nonlinear Stability
Spectral Analysis
Small Perturbations
Diffusion Coefficient
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Keywords

  • Long-time behavior
  • Shock fronts
  • Viscous conservation law

ASJC Scopus subject areas

  • Analysis

Cite this

Long-time behavior of scalar viscous shock fronts in two dimensions. / Goodman, Jonathan; Miller, Judith R.

In: Journal of Dynamics and Differential Equations, Vol. 11, No. 2, 1999, p. 255-277.

Research output: Contribution to journalArticle

Goodman, Jonathan ; Miller, Judith R. / Long-time behavior of scalar viscous shock fronts in two dimensions. In: Journal of Dynamics and Differential Equations. 1999 ; Vol. 11, No. 2. pp. 255-277.
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