Jamie M. Foster, Peter Gysbers, John R. King, and Dmitry E. Pelinovsky

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 di usion 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 confl uent 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.

Keywords:
Nonlinear diffusion equation, slow diffusion, strong absorption, self-similar solutions, invariant manifolds, reversing interface, anti-reversing interface, bifurcations, Kummer's differential equation.