9504177 Freidlin Abstract We study random perturbations of dynamical systems with conservation laws. The evolution of the first integral leads to a diffusion process on a graph corresponding to the first integral. This allows progress in a number of PDE problems with a small parameter. The two-dimensional Navier-Stocks equation with a large Reynolds number, for exampke, belongs to this class of problems. We study also large deviations for the diffusion-transmutation processes. These results help to describe the asymptotic behavior of wave fronts and other patterns in reaction-diffusion equations. Mathematical models of real processes sometimes,turn out to be too complicated for analysis. But very often some of the parameters included in the model are small (or large) in comparison with the others. This allows us to simplify the model and often to obtain the solution in a form convenient for applications. We study small random perturbations of dynamical systems, large scale approximation in reaction- diffusion models and other problems related to an interplay between random and deterministic factors.
