Long time existence for the heat equation with a noise term
We consider the equation \(u_ t=u_{xx}+u^{\gamma}\dot W\) for x on a finite interval, with Dirichlet boundary conditions. \(\dot W\) is spacetime white noise. The initial condition is continuous and nonnegative. We show existence and uniqueness for all time, provided \(1\leq \gamma <3/2\).
scientific article; zbMATH DE number 4205534