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arXiv · 1907.11799

Interface Development for the Nonlinear Degenerate Multidimensional Reaction-Diffusion Equations

Ugur G. Abdulla·Amna Abu Weden
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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 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.

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Ugur G. Abdulla, Amna Abu Weden. 2019-07-26. Interface Development for the Nonlinear Degenerate Multidimensional Reaction-Diffusion Equations. https://doi.org/10.1007/s00030-019-0606-2

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