Nonlocal evolution problems in thin domains
In this paper, we consider parabolic nonlocal problems in thin domains. Fix Ω ⊂ RN1 × RN2 and consider uϵ be the solution to (Formula presented.) with initial condition u(0, x) = u0(x) and a kernel of the form Jϵ(x) = J(x1,ϵx2) with J non-singular. This corresponds (via a simple change of variables)...
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| Autores principales: | , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00036811_v97_n12_p2059_Pereira |
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| Sumario: | In this paper, we consider parabolic nonlocal problems in thin domains. Fix Ω ⊂ RN1 × RN2 and consider uϵ be the solution to (Formula presented.) with initial condition u(0, x) = u0(x) and a kernel of the form Jϵ(x) = J(x1,ϵx2) with J non-singular. This corresponds (via a simple change of variables) to the usual nonlocal evolution problem (Formula presented.), in the thin domain (Formula presented.). Our main result says that there is a limit as (Formula presented.) of the solutions to our problem and that this limit, when we take its mean value in the (Formula presented.) -direction, is a solution to a limit nonlocal problem in the projected set Ω1 ⊂ RN1. © 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group. |
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