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

doi:10.1088/1361-6544/aad30b

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

School of Mathematics & Physics

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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 language	English
Article number	4621
Number of pages	28
Journal	Nonlinearity
Volume	31
Issue number	10
DOIs	https://doi.org/10.1088/1361-6544/aad30b
Publication status	Published - 31 Aug 2018

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Data availability for statement for 'Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption'.
Foster, J. (Creator), Gysbers, P. (Creator), King, J. R. (Creator) & Pelinovsky, D. E. (Creator), IOP Publishing, 12 Jul 2018
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N2 - 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.

AB - 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.

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JO - Nonlinearity

JF - Nonlinearity

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

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