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

Foster, J.M.; Gysbers, P.; King, J.R.; Pelinovsky, D.E.

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.

Citation

Foster, J., Gysbers, P., King, J., & Pelinovsky, D. (2018). Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption. Nonlinearity, 31(10), 4621-4648. https://doi.org/10.1088/1361-6544/aad30b

• Journal Article Type: Article
• Acceptance Date: Jul 12, 2018
• Online Publication Date: Aug 31, 2018
• Publication Date: Oct 30, 2018
• Deposit Date: Aug 10, 2018
• Publicly Available Date: Sep 1, 2019
• Print ISSN: 0951-7715
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 31
• Issue: 10
• Pages: 4621-4648
• DOI: https://doi.org/10.1088/1361-6544/aad30b
• Keywords: slow di usion equation, strong absorption, self-similar solutions, reversing interface, bifurcations, Kummer's di erential equation, matched asymptotic expansions
• Public URL: https://nottingham-repository.worktribe.com/output/988887
• Publisher URL: http://iopscience.iop.org/article/10.1088/1361-6544/aad30b
• Contract Date: Aug 10, 2018