Remarks on non-linear noise excitability of some stochastic heat equations

Mohammud Foondun, Mathew Joseph

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We consider nonlinear parabolic SPDEs of the form ∂tu= Δu+λσ(u)ẇ on the interval (0,L), where ẇ denotes space-time white noise, σ is Lipschitz continuous. Under Dirichlet boundary conditions and a linear growth condition on σ, we show that the expected L2-energy is of order exp[const×λ4] as λ→∞. This significantly improves a recent result of Khoshnevisan and Kim. Our method is very different from theirs and it allows us to arrive at the same conclusion for the same equation but with Neumann boundary condition. This improves over another result in Khoshnevisan and Kim.

Original languageEnglish
Pages (from-to)3429-3440
Number of pages12
JournalStochastic Processes and their Applications
Volume124
Issue number10
DOIs
Publication statusPublished - 13 May 2014
Externally publishedYes

Keywords

  • Stochastic partial differential equations
  • Neumann boundary condition

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