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

Abstract: I will consider the parabolic type stochastic partial differential equations with fractional Laplacian, which is the generator of a symmetric stable L'evy process. Under some conditions, namely faster than linear growth condition of a function and the initial condition, I will show non-existence of global random field solutions. These results are new and complement those of P. Chow, among others: 

P.-L. Chow. Unbounded positive solutions of nonlinear parabolic Ito equations. Commun.  Stoch. Anal., 3(2) (2009), 211—222.

P.-L. Chow. Explosive solutions of stochastic reaction-diffusion equations in mean  \(l_{p}\)-norm.  J. Differential Equations, 250(5) (2011), 2567—2580.