Communications in Mathematical Sciences

Volume 9 (2011)

Number 1

Relaxation to equilibrium in diffusive-thermal models with a strongly varying diffusion length-scale

Pages: 127 – 141

DOI: http://dx.doi.org/10.4310/CMS.2011.v9.n1.a6

Authors

Paul Clavin (Technopôle de Château-Gombert, Institut de Recherche sur les Phénomènes Hor Équilibre, Marseilles, France)

Laurent Masse (CEA Bruyères le Châtel, Ile de France, France)

Jean-Michel Roquejoffre (Institut de Mathématiques, Université Paul Sabatier, Toulouse, France)

Abstract

We consider reaction-diffusion equations with a strongly varying diffusion lengthscale. We provide a mathematical study of the relaxation towards the steady planar solution, in the context of infinitesimal disturbances whose wavelength is much shorter than the total thickness of the wave. The models under study are relevant in the description of ablation fronts encountered in inertial confinment fusion, when hydrodynamical effects are neglected.

Keywords

ablation front, relaxation, strongly varying diffusivity

2010 Mathematics Subject Classification

34E10, 34E20, 76R50

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