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arXiv · 1708.06286

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

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

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Jamie M. Foster, Peter Gysbers, John R. King, Dmitry E. Pelinovsky. 2017-08-21. Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption. https://doi.org/10.1088/1361-6544/aad30b

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