Interface Development for the Nonlinear Degenerate Multidimensional Reaction-Diffusion Equations
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 PDE \[ u_t-Δu^m +b u^β=0, \ x\in \mathbb{R}^N, 0 1, C,α, β>0, b \in \mathbb{R}$. Interface 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.
math.AP↗