Nonnegative solutions to stochastic heat equation with nonlinear drift

Abstract

We consider one-dimensional stochastic heat equation with nonlinear drift, ${\partial }_{t}u=\frac{1}{2}\Delta u+b(u)u+\sigma (u)\dot{W}(t,x)$, where $b:{\mathbb{R}}_{+}\to \mathbb{R}$ is a continuous function and $\sigma :{\mathbb{R}}_{+}\to \mathbb{R}$ is a continuous function with suitable property. We will construct nonnegative solutions to such SPDEs.

References in corpus (1)

• Branching random walks in random environment and super-Brownian motion in random environment