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.
"Small Diffusion and Fast Dying Out Asymptotics for Superprocesses as Non-Hamiltonian Quasiclassics for Evolution Equations." Electron. J. Probab. 6 1 - 16, 2001. https://doi.org/10.1214/EJP.v6-94