The long term behavior of a Stochastic PDE.
- Tribe, Roger
The one-dimensional heat equation driven by a particular white noise term is studied. From initial conditions with compact support, solutions retain this compact support and die out in finite time. The long term behavior of solutions from certain initial conditions can be described by a system of wavefronts whose positions move approximately as Brownian motions and such that two wavefronts annihilate when they collide.