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

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Foondun, Mohammud and Liu, Wei and Nane, Erkan (2019) Some non-existence results for a class of stochastic partial differential equations. Journal of Differential Equations, 266 (5). pp. 2575-2596. ISSN 0022-0396 (https://doi.org/10.1016/j.jde.2018.08.039)

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Abstract

Considerthe following stochastic partial differential equation, ∂tut(x)=Lut(x)+σ(ut(x))F˙(t,x)t>0andx∈Rd. The operator L is thegenerator of a strictly stable process and F˙ is the random forcing term whichis assumed to be Gaussian. Under some additional conditions, most notably on σ and the initial condition, weshow non-existence of global random field solutions. Our results are new andcomplement earlier works.

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