Interface development for the nonlinear degenerate multidimensional reaction–diffusion equations

Abstract

This paper presents a full classification of the short-time behavior of the interfaces in the Cauchy problem for the nonlinear second order degenerate parabolic PDEInterface surface t = η(x) may shrink, expand or remain stationary depending on the relative strength of the diffusion and reaction terms near the boundary of support, expressed in terms of the parameters m, β, α, sign b and C. In all cases we prove explicit formula for the interface asymptotics, and local solution near the interface.