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

Jamie Foster, P. Gysbers, J. R. King, D. 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 {particular points in parameter space (characterizing the exponents in the diffusion and absorption terms)} where the confluent hypergeometric functions satisfying Kummer's differential equation {truncate to finite polynomials}. A two-scale asymptotic method is employed to obtain the local dependencies of the self-similar reversing interfaces near the bifurcation points. The asymptotic results are shown to be in excellent agreement with numerical approximations of the self-similar solutions.
Original languageEnglish
Article number4621
Number of pages28
JournalNonlinearity
Volume31
Issue number10
DOIs
Publication statusPublished - 31 Aug 2018

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