Jesus Ildefonso Diaz, David Gomez-Castro, Tatiana A. Shaposhnikova, Maria N. Zubova
Abstract:
Our main interest in this article is the study of homogenized limit of a
parabolic equation with a nonlinear dynamic boundary condition of the
micro-scale model set on a domain with periodically place particles.
We focus on the case of particles (or holes) of critical diameter with respect
to the period of the structure.
Our main result proves the weak convergence of the sequence of solutions of
the original problem to the solution of a reaction-diffusion parabolic problem
containing a "strange term".
The novelty of our result is that this term is a nonlocal memory solving an ODE.
We prove that the resulting system satisfies a comparison principle.
Submitted March 10, 2019. Published June 4, 2019.
Math Subject Classifications: 35B27, 35K57.
Key Words: Critically scaled homogenization; perforated media;
dynamical boundary conditions; strange term; nonlocal memory reaction.
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Jesús Ildefonso Díaz Instituto de Matematica Interdisciplinar Universidad Complutense de Madrid 28040 Madrid, Spain email: jidiaz@ucm.es |
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David Gómez-Castro Instituto de Matematica Interdisciplinar Universidad Complutense de Madrid 28040 Madrid, Spain email: dgcastro@ucm.es |
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Tatiana A. Shaposhnikova Faculty of Mechanics and Mathematics Moscow State University Moscow, Russia email: shaposh.tan@mail.ru |
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Maria N. Zubova Faculty of Mechanics and Mathematics Moscow State University Moscow, Russia email: zubovnv@mail.ru |
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