Stabilization of partial differential equations by noise

Abstract

We provide an example of a class of partial differential equations being stabilized (in terms of Lyapunov exponents) by noise. In particular, we show that the stability of the heat equation can be improved by adding a stochastic term to the equation. We also give an example of an unstable PDE made stable by noise.Lyapunov exponents Stochastic partial differential equations Partial differential equations Heat equation