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Article Dans Une Revue Annales de l'Institut Henri Poincaré Année : 2013

Homogenization and correctors for monotone problems in cylinders of small diameter

Résumé

In this paper we study the homogenization of monotone diffusion equations posed in an N-dimensional cylinder which converges to a (one-dimensional) segment line. In other terms, we pass to the limit in diffusion monotone equations posed in a cylinder whose diameter tends to zero, when simultaneously the coefficients of the equations (which are not necessarily periodic) are also varying. We obtain a limit system in both the macroscopic (one-dimensional) variable and the microscopic variable. This system is nonlocal. From this system we obtain by elimination an equation in the macroscopic variable which is local, but in contrast with usual results, the operator depends on the right-hand side of the equations. We also obtain a corrector result, i.e. an approximation of the gradients of the solutions in the strong topology of the space L-P in which the monotone operators are defined.

Dates et versions

hal-01256459 , version 1 (14-01-2016)

Identifiants

Citer

Juan Casado-Diaz, François Murat, Ali Sili. Homogenization and correctors for monotone problems in cylinders of small diameter. Annales de l'Institut Henri Poincaré, 2013, 30 (3), pp.519-545. ⟨10.1016/j.anihpc.2012.10.004⟩. ⟨hal-01256459⟩
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