Homogenization of a reaction-diffusion-advection problem in an evolving micro-domain and including nonlinear boundary conditions
We consider a reaction-diffusion-advection problem in a perforated medium, with nonlinear reactions in the bulk and at the microscopic boundary, and slow diffusion scaling. The microstructure changes in time; the microstructural evolution is known a priori. The aim of the paper is the rigorous deriv...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
23 April 2021
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| In: |
Journal of differential equations
Year: 2021, Volume: 289, Pages: 95-127 |
| ISSN: | 1090-2732 |
| DOI: | 10.1016/j.jde.2021.04.013 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jde.2021.04.013 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0022039621002436 
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| Author Notes: | M. Gahn, M. Neuss-Radu, I.S. Pop |
| Summary: | We consider a reaction-diffusion-advection problem in a perforated medium, with nonlinear reactions in the bulk and at the microscopic boundary, and slow diffusion scaling. The microstructure changes in time; the microstructural evolution is known a priori. The aim of the paper is the rigorous derivation of a homogenized model. We use appropriately scaled function spaces, which allow us to show compactness results, especially regarding the time-derivative and we prove strong two-scale compactness results of Kolmogorov-Simon-type, which allow to pass to the limit in the nonlinear terms. The derived macroscopic model depends on the micro- and the macro-variable, and the evolution of the underlying microstructure is approximated by time- and space-dependent reference elements. |
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| Item Description: | Gesehen am 01.07.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1090-2732 |
| DOI: | 10.1016/j.jde.2021.04.013 |