Phasefield theory for fractional diffusion-reaction equations and applications
Imbert, Cyril; Souganidis, Panagiotis E. (2009), Phasefield theory for fractional diffusion-reaction equations and applications. https://basepub.dauphine.fr/handle/123456789/7218
TypeDocument de travail / Working paper
External document linkhttp://arxiv.org/abs/0907.5524v1
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Abstract (EN)This paper is concerned with diffusion-reaction equations where the classical diffusion term, such as the Laplacian operator, is replaced with a singular integral term, such as the fractional Laplacian operator. As far as the reaction term is concerned, we consider bistable non-linearities. After properly rescaling (in time and space) these integro-differential evolution equations, we show that the limits of their solutions as the scaling parameter goes to zero exhibit interfaces moving by anisotropic mean curvature. The singularity and the unbounded support of the potential at stake are both the novelty and the challenging difficulty of this work.
Subjects / Keywordsfractional diffusion-reaction equations; traveling wave; phasefield theory; anisotropic mean curvature motion; fractional Laplacian; Green-Kubo type formulae
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