On the behaviour of stochastic heat equations on bounded domains

Mohammud Foondun, Eulalia Nualart

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Consider the following equation ∂tut(x) = 1 2 ∂xxut(x) + λσ(ut(x))W˙ (t, x) on an interval. Under Dirichlet boundary condition, we show that in the long run, the second moment of the solution grows exponentially fast if λ is large enough. But if λ is small, then the second moment eventually decays exponentially. If we replace the Dirichlet boundary condition by the Neumann one, then the second moment grows exponentially fast no matter what λ is. We also provide various extensions.

Original languageEnglish
Pages (from-to)551-571
Number of pages21
JournalAlea
Volume12
Issue number2
Publication statusPublished - 2015
Externally publishedYes

Keywords

  • stochastic partial differential equations
  • Dirichlet boundary condition

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