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
Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diusion 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.
Nonlinear diffusion equation, slow diffusion, strong absorption, self-similar solutions,
invariant manifolds, reversing interface, anti-reversing interface, bifurcations, Kummer's differential equation.