Finite-time blowup and existence of global positive solutions of a semi-linear SPDE

Marco Dozzi, José Alfredo Lopez

We consider stochastic equations of the prototype $du(t,x)=(\Delta u(t,x)+u(t,x{)}^{1+\beta })dt+\kappa u(t,x)d{W}_t$ on a smooth domain $D\subset {\mathrm{I}\mathrm{R}}^d$, with Dirichlet…