Two results concerning asymptotic behavior of solutions of the Burgers equation with force

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Abstract

We consider the Burgers equation with an external force. For the case of the force periodic in space and time we prove the existence of a solution periodic in space and time which is the limit of a wide class of solutions as t → ∞. If the force is the product of a periodic function of x and white noise in time, we prove the existence of an invariant distribution concentrated on the space of space-periodic functions which is the limit of a wide class of distributions as t → ∞.

Original languageEnglish (US)
Pages (from-to)1-12
Number of pages12
JournalJournal of Statistical Physics
Volume64
Issue number1-2
DOIs
StatePublished - Jul 1 1991

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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