White noise perturbation of the viscous shock fronts of the burgers equation

J. Wehr, J. Xin

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

We study the front dynamics of solutions of the initial value problem of the Burgers equation with initial data being the viscous shock front plus the white noise perturbation. In the sense of distribution, the solutions propagate with the same speed as the unperturbed front, however, the front location is random and satisfies a central limit theorem with the variance proportional to the time t, as t goes to infinity. With probability arbitrarily close to one, the front width is O(1) for large time.

Original languageEnglish (US)
Pages (from-to)183-203
Number of pages21
JournalCommunications in Mathematical Physics
Volume181
Issue number1
DOIs
StatePublished - Jan 1 1996

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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