On a Stefan-type model arising in ecology

Dedicated to the memory of Anatolii Kalashnikov
https://doi.org/10.1016/j.aml.2003.02.014Get rights and content
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Abstract

We discuss the dispersal of a chemical, emitted from a point source, into a reacting medium. The diffusion and reaction are such that a front emerges, so that at all times the chemical remains confined to a bounded domain around the source. We focus on the final stationary state which is a non-standard Stefan-type boundary value problem for an Emden–Fowler equation. We prove its existence and uniqueness and obtain, analytically as well as numerically, bounds for the location of the front and for the concentration profile.

Keywords

Reaction–diffusion
Free boundary
Emden–Fowler equation
Stefan problem

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