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 language | English |
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Pages (from-to) | 2017-2050 |
Number of pages | 34 |
Journal | SIAM Journal on Applied Dynamical Systems |
Volume | 15 |
Issue number | 4 |
Early online date | 1 Nov 2016 |
DOIs | |
Publication status | Published - Nov 2016 |
Keywords
- nonlinear diffusion equation
- slow diffusion
- strong absorption
- self-similar solutions
- invariant manifolds
- reversing interface
- antireversing interface