Pulsating traveling waves in the singular limit of a reaction-diffusion system in solid combustion
R. Monneau, G. S. Weiss (2009)
Annales de l'I.H.P. Analyse non linéaire
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Displaying similar documents to “Traveling waves with paraboloid like interfaces for balanced bistable dynamics”
Pulsating traveling waves in the singular limit of a reaction-diffusion system in solid combustion
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Annales de l'I.H.P. Analyse non linéaire
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We discuss the asymptotics of the parabolic Ginzburg-Landau equation in dimension Our only asumption on the initial datum is a natural energy bound. Compared to the case of “well-prepared” initial datum, this induces possible new energy modes which we analyze, and in particular their mutual interaction. The two dimensional case is qualitatively different and requires a separate treatment.
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Nicolas Forcadel, Aurélien Monteillet (2009)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove existence of minimizing movements for the dislocation dynamics evolution law of a propagating front, in which the normal velocity of the front is the sum of a non-local term and a mean curvature term. We prove that any such minimizing movement is a weak solution of this evolution law, in a sense related to viscosity solutions of the corresponding level-set equation. We also prove the consistency of this approach, by showing that any minimizing movement coincides with the smooth...
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Annales de l'I.H.P. Analyse non linéaire
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Homogenization of periodic non self-adjoint problems with large drift and potential
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ESAIM: Control, Optimisation and Calculus of Variations
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We consider the homogenization of both the parabolic and eigenvalue problems for a singularly perturbed convection-diffusion equation in a periodic medium. All coefficients of the equation may vary both on the macroscopic scale and on the periodic microscopic scale. Denoting by the period, the potential or zero-order term is scaled as and the drift or first-order term is scaled as . Under a structural hypothesis on the first cell eigenvalue, which is assumed to admit a unique minimum...