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

Foster, J.M. and Gysbers, P. and King, J.R. and Pelinovsky, D.E. (2018) Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption. Nonlinearity, 31 (10). pp. 4621-4648. ISSN 0951-7715

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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.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1088/1361-6544/aad30b
Depositing User: Lashkova, Mrs Olga
Date Deposited: 07 Sep 2018 09:37
Last Modified: 31 Aug 2019 04:30
URI: http://eprints.nottingham.ac.uk/id/eprint/53818

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