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Asymptotic analysis of a multiscale parabolic problem with a rough fast oscillating interface

  • Patrizia Donato
  • Editha C. Jose
  • Daniel Onofrei
Original
  • 30 Downloads

Abstract

This paper is concerned with the well posedness and homogenization for a multiscale parabolic problem in a cylinder Q of \({\mathbb {R}}^N \). A rapidly oscillating non-smooth interface inside Q separates the cylinder in two heterogeneous connected components. The interface has a periodic microstructure, and it is situated in a small neighborhood of a hyperplane which separates the two components of Q. The problem models a time-dependent heat transfer in two heterogeneous conducting materials with an imperfect contact between them. At the interface, we suppose that the flux is continuous and that the jump of the solution is proportional to the flux. On the exterior boundary, homogeneous Dirichlet boundary conditions are prescribed. We also derive a corrector result showing the accuracy of our approximation in the energy norm.

Keywords

Parabolic problem Homogenization Heat propagation Rough interface Correctors 

Mathematics Subject Classification

35J75 35J65 35B27 

Notes

Acknowledgements

The work of E.J. was funded by the UP System Enhanced Creative Work and Research Grant (EWCRG 2016-1-010), while that of D.O. was supported by the USAID STRIDE Visiting U.S. Professors Program. The authors were able to visit each other through the support of the following: Erasmus Mundus (IMPAKT) Staff Mobility Program (P.D. and E.J.) and Universite de Rouen and University of Houston (D.O. and E.J.).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Patrizia Donato
    • 1
  • Editha C. Jose
    • 2
  • Daniel Onofrei
    • 3
  1. 1.Laboratoire de Mathématiques Raphaël Salem, UMR CNRS 6085Université de Rouen NormandieSaint Étienne de RouvrayFrance
  2. 2.Institute of Mathematical Sciences and PhysicsUniversity of the Philippines Los BañosLos BanosPhilippines
  3. 3.Department of MathematicsUniversity of HoustonHoustonUSA

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