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

Jonathan Goodman, Judith R. Miller

Research output: Contribution to journalArticlepeer-review


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
Issue number2
StatePublished - 1999


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

ASJC Scopus subject areas

  • Analysis


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