Small Diffusion and Fast Dying Out Asymptotics for Superprocesses as Non-Hamiltonian Quasiclassics for Evolution Equations

Abstract

The small diffusion and fast dying out asymptotics is calculated for nonlinear equations of a class of superprocesses on manifolds, and the corresponding logarithmic limit of the solution is shown to be given by a solution of a certain problem of calculus of variations with a non-additive (and non-integral) functional.