Interface dynamics of the porous medium equation with a bistable reaction term

Abstract : We consider a degenerate partial differential equation arising in population dynamics, namely the porous medium equation with a bistable reaction term. We study its asymptotic behavior as a small parameter, related to the thickness of a diffuse interface, tends to zero. We prove the rapid formation of transition layers which then propagate. We prove the convergence to a sharp interface limit whose normal velocity, at each point, is that of the underlying degenerate travelling wave.
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https://hal.archives-ouvertes.fr/hal-00609087
Contributor : Matthieu Alfaro <>
Submitted on : Monday, July 18, 2011 - 10:24:46 AM
Last modification on : Tuesday, December 4, 2018 - 4:48:04 PM
Long-term archiving on : Wednesday, October 19, 2011 - 2:21:53 AM

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  • HAL Id : hal-00609087, version 1
  • ARXIV : 1107.3543

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Matthieu Alfaro, Danielle Hilhorst. Interface dynamics of the porous medium equation with a bistable reaction term. Asymptotic Analysis, IOS Press, 2012, pp.76 (2012), 35-48. ⟨hal-00609087⟩

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