Singular limit for reactive diffusive transport through an array of thin channels in case of critical diffusivity

• Verfasst von: Gahn, Markus [VerfasserIn]
• Verfasst von: Neuss-Radu, Maria [VerfasserIn]
• Titel: Singular limit for reactive diffusive transport through an array of thin channels in case of critical diffusivity
• Verf.angabe: Markus Gahn, Maria Neuss-Radu
• E-Jahr: 2021
• Jahr: November 1, 2021
• Umfang: 28 S.
• Fussnoten: Gesehen am 24.02.2022
• Titel Quelle: Enthalten in: Multiscale modeling & simulation
• Ort Quelle: Philadelphia, Pa. : SIAM, 2003
• Jahr Quelle: 2021
• Band/Heft Quelle: 19(2021), 4, Seite 1573-1600
• ISSN Quelle: 1540-3467
• DOI: doi:10.1137/21M1390505
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 35B27
• Sach-SW: 35K57
• Sach-SW: 35Q92
• Sach-SW: array of channels
• Sach-SW: effective transmission conditions
• Sach-SW: homogenization
• Sach-SW: nonlinear boundary conditions
• Sach-SW: reaction-diffusion equation
• Sach-SW: two-scale convergence
• K10plus-PPN: 1793861706

Abstract

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.