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

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.

reaction-diffusion equation ; Robin boundary condition ; different orders of compression ; oscillating boundary ; homogenization

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