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

Abstract

© 2015, American Mathematical Society. We consider nonlinear parabolic SPDEs of the form ∂ t u = − (−Δ) α/2 u + 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.