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We consider the slow nonlinear diffusion equation subject to a constantabsorption rate and construct local self-similar solutions for reversing (andanti-reversing) interfaces, where an initially advancing (receding) interfacegives way to a receding (advancing) one. We use an approach based on invariantmanifolds, which allows us to determine the required asymptotic behaviour forsmall and large values of the concentration. We then `connect' the requisiteasymptotic behaviours using a robust and accurate numerical scheme. By doingso, we are able to furnish a rich set of self-similar solutions for bothreversing and anti-reversing interfaces.

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