Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption
Pattern Formation and Solitons
2018-09-26 v1 Mathematical Physics
Analysis of PDEs
Dynamical Systems
math.MP
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.
Keywords
Cite
@article{arxiv.1708.06286,
title = {Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption},
author = {Jamie M. Foster and Peter Gysbers and John R. King and Dmitry E. Pelinovsky},
journal= {arXiv preprint arXiv:1708.06286},
year = {2018}
}
Comments
20 pages, 4 figures