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

Jan Wehr, J. Xin

Research output: Contribution to journalArticle

14 Citations (Scopus)

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
StatePublished - 1996

Fingerprint

Burger equation
shock fronts
Burgers Equation
white noise
White noise
Shock
Perturbation
perturbation
boundary value problems
infinity
theorems
Central limit theorem
Initial Value Problem
Directly proportional
Infinity

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

White noise perturbation of the viscous shock fronts of the burgers equation. / Wehr, Jan; Xin, J.

In: Communications in Mathematical Physics, Vol. 181, No. 1, 1996, p. 183-203.

Research output: Contribution to journalArticle

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