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arXiv · 1506.05058

Self-similar solutions for reversing interfaces in the nonlinear diffusion equation with constant absorption

Jamie M. Foster·Dmitry E. Pelinovsky
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Abstract

We consider the slow nonlinear diffusion equation subject to a constant 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.

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Jamie M. Foster, Dmitry E. Pelinovsky. 2015-06-16. Self-similar solutions for reversing interfaces in the nonlinear diffusion equation with constant absorption. https://arxiv.org/abs/1506.05058

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