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

Foondun, Mohammud; Parshad, Rana

doi:10.1090/proc/12036

On non-existence of global solutions to a class of stochastic heat equations
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by Mohammud Foondun and Rana D. Parshad

Proc. Amer. Math. Soc. 143 (2015), 4085-4094

DOI: https://doi.org/10.1090/proc/12036

Published electronically: April 6, 2015

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Abstract:

We consider nonlinear parabolic SPDEs of the form $\partial _t u=-$ $(-\Delta )^{\alpha /2} u + b(u) +\sigma (u)\dot w$, where $\dot w$ denotes space-time white noise. The functions $b$ and $\sigma$ 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.

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