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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 Connect in order to contact the contributor
Submitted on : Monday, July 18, 2011 - 10:24:46 AM
Last modification on : Monday, October 11, 2021 - 1:22:30 PM
Long-term archiving on: : Wednesday, October 19, 2011 - 2:21:53 AM

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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, 76 (1), pp.35-48. ⟨10.3233/ASY-2011-1067⟩. ⟨hal-00609087⟩

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