Singular limit for reactive diffusive transport through an array of thin channels in case of critical diffusivity
We consider a nonlinear reaction-diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order epsilon and the equation inside the layer depends on the parameter epsil...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
November 1, 2021
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| In: |
Multiscale modeling & simulation
Year: 2021, Volume: 19, Issue: 4, Pages: 1573-1600 |
| ISSN: | 1540-3467 |
| DOI: | 10.1137/21M1390505 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/21M1390505 Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/21M1390505 
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| Author Notes: | Markus Gahn, Maria Neuss-Radu |
| Summary: | We consider a nonlinear reaction-diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order epsilon and the equation inside the layer depends on the parameter epsilon. We consider the critical scaling of the diffusion coefficients in the channels and nonlinear Neumann boundary condition on the channels' lateral boundaries. We derive effective models in the limit epsilon to 0, when the channel domain is replaced by an interface Sigma between the two bulk domains. Due to the critical size of the diffusion coefficients, we obtain jumps for the solution and its normal fluxes across Sigma, involving the solutions of local cell problems on the reference channel in every point of the interface Sigma. |
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| Item Description: | Gesehen am 24.02.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1540-3467 |
| DOI: | 10.1137/21M1390505 |