Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption

Abstract

Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show that such bifurcations occur at the bifurcation points, at which the confluent hypergeometric functions satisfying Kummer's differential equation is truncated into a finite polynomial. A two-scale asymptotic method is employed to obtain the asymptotic dependencies of the self-similar reversing interfaces near the bifurcation points. The asymptotic results are shown to be in excellent agreement with numerical computations.

20 pages, 4 figures