Jamie M. Foster and Dmitry E. Pelinovsky

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

SIAM Journal of Applied Dynamical Systems 15, 2017-2050 (2016)

Abstract: We consider the slow nonlinear diffusion equation subject to a strong absorption rate and construct local self-similar solutions for reversing (and antireversing) 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 behavior for small and large values of the concentration. We then “connect” the requisite asymptotic behaviors 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 antireversing interfaces. The stability of these self-similar solutions is validated against direct numerical simulation in the case of constant absorption

Nonlinear diffusion equation, slow diffusion, strong absorption, self-similar solutions, invariant manifolds, reversing interface, anti-reversing interface.