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

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 dir...

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Bibliographic Details
Published in:European journal of applied mathematics 2023-10, Vol.34 (5), p.1099-1132
Main Authors: King, John R., Richardson, Giles W., Foster, Jamie M.
Format: Article
Language:English
Subjects:
Absorption
Applied mathematics
Asymptotic methods
Asymptotic properties
Behavior
Boundary conditions
Diffusion rate
Extinction
Interfaces
Self-similarity
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Summary: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.
ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792523000098