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

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

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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 antireversing), when an interface detaches from a 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 are provided. Self-similar solutions, both of the full equation and of its asymptotic limits, play a central role in the analysis.
Original languageEnglish
Number of pages34
JournalEuropean Journal of Applied Mathematics
Early online date14 Jun 2023
DOIs
Publication statusEarly online - 14 Jun 2023

Keywords

  • slow diffusion
  • strong absorption
  • porous medium equation
  • asymptotic analysis
  • interface behaviour

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