Some non-existence results for a class of stochastic partial differential equations

Mohammud Foondun, Wei Liu, Erkan Nane

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Abstract

Consider the following stochastic partial differential equation,

tut(x)=Lut(x)+σ(ut(x))F˙(t,x)t>0andxRd.

The operator L is the generator of a strictly stable process and F˙ is the random forcing term which is assumed to be Gaussian. Under some additional conditions, most notably on σ and the initial condition, we show non-existence of global random field solutions. Our results are new and complement earlier works.

Original languageEnglish
JournalJournal of Differential Equations
Publication statusAccepted/In press - 21 Dec 2017

Keywords

  • probability
  • partial differential equation

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