Asymptotics for scaled Kramers-Smoluchowski equations in several dimensions with general potentials

In this paper, we generalize the results of Evans and Tabrizian, by deriving asymptotics for the time-rescaled Kramers-Smoluchowski equations, in the case of a general non-symmetric potential function with multiple wells. The asymptotic limit is described by a system of reaction-diffusion equations whose coefficients are determined by the Kramers constants at the saddle points of the potential function and the Hessians of the potential function at global minima.