Burgers equation with random forcing in noncompact setting
The Burgers equation is one of the basic nonlinear evolutionary PDEs.
The study of ergodic properties of the Burgers equation with random forcing
began in the 1990's. The natural approach is based on the analysis of
optimal paths in the random landscape generated by the random force potential.
For a long time only compact cases of the Burgers dynamics on a circle or
bounded interval were understood well. In this talk I will discuss the
Burgers dynamics on the entire real line with no compactness or periodicity
assumption on the random forcing. The main result is the description of the
ergodic components and existence of a global attracting random solution in each
component. The proof is based on ideas from the theory of first or last
passage percolation. This is a joint work with Eric Cator and Kostya Khanin.