ON NON-EXISTENCE OF GLOBAL SOLUTIONS TO A CLASS OF STOCHASTIC HEAT EQUATIONS

Mohammud Foondun, Rana Parshad

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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 (US)
Pages (from-to)4085-4094
Number of pages10
JournalProceedings of the American Mathematical Society
Volume143
Issue number9
DOIs
StatePublished - 2015

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

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