Self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption

Jamie Foster, Dmitry E. Pelinovsky

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Abstract

We consider the slow nonlinear diffusion equation subject to a strong absorption rate and construct local self-similar solutions for reversing (and anti-reversing) interfaces, where an initially advancing (receding) interface gives way to a receding (advancing) one. We use an approach based on invariant manifolds, which allows us to determine the required asymptotic behaviour for small and large values of the concentration. We then `connect' the requisite asymptotic behaviours using a robust and accurate numerical scheme. By doing so, we are able to furnish a rich set of self-similar solutions for both reversing and anti-reversing interfaces. The stability of these self-similar solutions is validated against direct numerical simulation in the case of constant absorption.
Original languageEnglish
Pages (from-to)2017-2050
Number of pages34
JournalSIAM Journal on Applied Dynamical Systems
Volume15
Issue number4
Early online date1 Nov 2016
DOIs
Publication statusPublished - Nov 2016

Keywords

  • nonlinear diffusion equation
  • slow diffusion
  • strong absorption
  • self-similar solutions
  • invariant manifolds
  • reversing interface
  • antireversing interface

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