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

Foondun, Mohammud and Liu, Wei and Nane, Erkan (2017) Some non-existence results for a class of stochastic partial differential equations. Journal of Differential Equations. ISSN 0022-0396 (In Press)

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    Abstract

    Consider the following stochastic partial differential equation, ∂tut(x)=Lut(x)+σ(ut(x))F˙(t,x)t>0andx∈Rd. 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.