Reaction–diffusion problem in a thin domain with oscillating boundary and varying order of thickness

Abstract

In this paper, we study a reaction–diffusion problem in a thin domain with varying order of thickness. Motivated by the applications, we assume the oscillating behavior of the boundary and prescribe the Robin-type boundary condition simulating the reaction catalyzed by the upper wall. Using the appropriate functional setting and the unfolding operator method, we rigorously derive lower-dimensional approximation of the governing problem. Five different limit problems have been obtained by comparing the magnitude of the reaction mechanism with the variation in domain’s thickness.

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Acknowledgements

The first author of this work has been supported by CAPES 88887.507830/2020-00. The second author has been supported by the Croatia Science Foundation under the project MultiFM (IP-2019-04-1140). The third author has been partially supported by the Croatia Science Foundation under the Project MultiFM (IP-2019-04-1140) and CNPq 303253/2017-7 (Brazil).

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Correspondence to Igor Pažanin.

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Nakasato, J.C., Pažanin, I. & Pereira, M.C. Reaction–diffusion problem in a thin domain with oscillating boundary and varying order of thickness. Z. Angew. Math. Phys. 72, 5 (2021). https://doi.org/10.1007/s00033-020-01436-z

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Keywords

  • Reaction–diffusion equation
  • Robin boundary condition
  • Different orders of compression
  • Oscillating boundary
  • Homogenization

Mathematics Subject Classification

  • 35B25
  • 35B40
  • 35J25