Degeneration of effective diffusion in the presence of periodic potential
Serguei M. Kozlov, Andrei L. Piatnitski (1996)
Annales de l'I.H.P. Probabilités et statistiques
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Serguei M. Kozlov, Andrei L. Piatnitski (1996)
Annales de l'I.H.P. Probabilités et statistiques
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G. Barles, L. Bronsard, P. E. Souganidis (1992)
Annales de l'I.H.P. Analyse non linéaire
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Bianca Stroffolini (2007)
ESAIM: Control, Optimisation and Calculus of Variations
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We study an homogenization problem for Hamilton-Jacobi equations in the geometry of Carnot Groups. The tiling and the corresponding notion of periodicity are compatible with the dilatations of the Group and use the Lie bracket generating property.
J. Lederer, R. Lewandowski (2007)
Annales de l'I.H.P. Analyse non linéaire
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Henry Berestycki, François Hamel, Nikolai Nadirashvili (2005)
Journal of the European Mathematical Society
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This paper is devoted to some nonlinear propagation phenomena in periodic and more general domains, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a follow-up of the article [7]. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of...
Guillaume Bal (2001)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper deals with the homogenization of a spectral equation posed in a periodic domain in linear transport theory. The particle density at equilibrium is given by the unique normalized positive eigenvector of this spectral equation. The corresponding eigenvalue indicates the amount of particle creation necessary to reach this equilibrium. When the physical parameters satisfy some symmetry conditions, it is known that the eigenvectors of this equation can be approximated by the product...