On non-existence of global solutions to a class of stochastic heat equations

Mohammud Foondun, Rana D. Parshad

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We consider nonlinear parabolic SPDEs of the form ∂tu = − (−Δ)α/2u + b(u) + σ(u)ẇ, where ẇ denotes space-time white noise. The functions b and σ are both locally Lipschitz continuous. Under some suitable conditions on the parameters of this SPDE, we show that the above equation has no random-field solution. This complements recent works of Khoshnevisan and his coauthors.

Original languageEnglish
Pages (from-to)4085-4094
Number of pages10
JournalProceedings of the American Mathematical Society
Volume143
Issue number9
DOIs
Publication statusPublished - 6 Apr 2015
Externally publishedYes

Keywords

  • liapounov exponents
  • stable processes
  • stochastic partial differential equations
  • weak intermittence

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