Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties

King, John R.; Richardson, Giles W.; Foster, Jamie M.

Abstract

The dynamics of interfaces in slow diffusion equations with strong absorption are studied. Asymptotic methods are used to give descriptions of the behaviour local to a comprehensive range of possible singular events that can occur in any evolution. These events are: when an interface changes its direction of propagation (reversing and anti-reversing), when an interface detaches from an absorbing obstacle (detaching), when two interfaces are formed by film rupture (touchdown) and when the solution undergoes extinction. Our account of extinction and self-similar reversing and anti-reversing is built upon previous work; results on non-self-similar reversing and anti-reversing and on the various types of detachment and touchdown are developed from scratch. In all cases, verification of the asymptotic results against numerical solutions to the full PDE is provided. Self-similar solutions, both of the full equation and of its asymptotic limits, play a central role in the analysis.

Citation

King, J. R., Richardson, G. W., & Foster, J. M. (2023). Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties. European Journal of Applied Mathematics, 34(5), 1099-1132. https://doi.org/10.1017/S0956792523000098

• Journal Article Type: Article
• Acceptance Date: Mar 10, 2023
• Online Publication Date: Jun 14, 2023
• Publication Date: 2023-10
• Deposit Date: Apr 6, 2023
• Publicly Available Date: Dec 15, 2023
• Journal: European Journal of Applied Mathematics
• Print ISSN: 0956-7925
• Electronic ISSN: 1469-4425
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 34
• Issue: 5
• Pages: 1099-1132
• DOI: https://doi.org/10.1017/S0956792523000098
• Keywords: Slow diffusion; strong absorption; porous medium equation; asymptotic analysis; interface behaviour
• Public URL: https://nottingham-repository.worktribe.com/output/19292613
• Publisher URL: https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/interface-behaviour-of-the-slow-diffusion-equation-with-strong-absorption-intermediateasymptotic-properties/E0B9CC708CE737A288B0F78FA70295AE
• Additional Information: Copyright: © The Author(s), 2023. Published by Cambridge University Press; License: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.; Free to read: This content has been made available to all.