Probability and Mathematical Physics Seminar

We consider solutions to the viscous Burgers' equation with a random forcing in one dimension. We show that when the forcing is a spatial derivative of a smooth space-time stationary random field, there exist space-time stationary solutions. We also show that they describe the long time behavior for a reasonable class of initial conditions. These space-time stationary solutions can, in turn, be used to construct shock-like time-stationary solutions that connect such space-stationary states as their limits at infinity. This is a joint work with A. Dunlap and C. Graham.