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Correctors and error estimates for reaction-diffusion processes through thin heterogeneous layers in case of homogenized equations with interface diffusion. (English) Zbl 1450.35038

The authors have proven previously the periodic homogenization of the problem at hand. Now, they construct approximations of the microscopic solution of their nonlinear reaction-diffusion equation posed in a domain made of two bulk-domains separated by a thin layer with periodic internal structure. They used them to ensure the main result: a proof of corrector estimates, i.e. explicit convergence speeds in suitable norms comparing between the solution of the microscopic problem and the one for the upscaled problem.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35K57 Reaction-diffusion equations
35C20 Asymptotic expansions of solutions to PDEs
35B45 A priori estimates in context of PDEs
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