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 |
|---|---|
| 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