EFFECTIVE INTERFACE CONDITIONS FOR PROCESSES THROUGH THIN HETEROGENEOUS LAYERS WITH NONLINEAR TRANSMISSION AT THE MICROSCOPIC BULK-LAYER INTERFACE

Gahn M, Neuss-Radu M, Knabner P (2018)

Publication Language: English

Publication Status: Published

Publication Type: Journal article

Publication year: 2018

Journal

Networks and Heterogeneous Media American Institute of Mathematical Sciences (AIMS)

Publisher: AMER INST MATHEMATICAL SCIENCES-AIMS

Book Volume: 13

Pages Range: 609-640

Journal Issue: 4

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_2018/2018_GahnNeussraduKn_EffectInterfCondForProcThrouThinHeterogenLayerWthNonlinearTransmissAtTeMicroscBulklayerInterface

DOI: 10.3934/nhm.2018028

Abstract

In this paper, we consider a system of reaction-diffusion equations in a domain consisting of two bulk regions separated by a thin layer with thickness of order epsilon and a periodic heterogeneous structure. The equations inside the layer depend on epsilon and the diffusivity inside the layer on an additional parameter gamma is an element of [-1, 1]. On the bulk-layer interface, we assume a nonlinear Neumann-transmission condition depending on the solutions on both sides of the interface. For epsilon -> 0, when the thin layer reduces to an interface Sigma between two bulk domains, we rigorously derive macroscopic models with effective conditions across the interface Sigma. The crucial part is to pass to the limit in the nonlinear terms, especially for the traces on the interface between the different compartments. For this purpose, we use the method of two-scale convergence for thin heterogeneous layers, and a Kolmogorov-type compactness result for Banach valued functions, applied to the unfolded sequence in the thin layer.

Authors with CRIS profile

Markus Gahn Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Maria Neuß Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

How to cite

APA:

Gahn, M., Neuss-Radu, M., & Knabner, P. (2018). EFFECTIVE INTERFACE CONDITIONS FOR PROCESSES THROUGH THIN HETEROGENEOUS LAYERS WITH NONLINEAR TRANSMISSION AT THE MICROSCOPIC BULK-LAYER INTERFACE. Networks and Heterogeneous Media, 13(4), 609-640. https://doi.org/10.3934/nhm.2018028

MLA:

Gahn, Markus, Maria Neuss-Radu, and Peter Knabner. "EFFECTIVE INTERFACE CONDITIONS FOR PROCESSES THROUGH THIN HETEROGENEOUS LAYERS WITH NONLINEAR TRANSMISSION AT THE MICROSCOPIC BULK-LAYER INTERFACE." Networks and Heterogeneous Media 13.4 (2018): 609-640.

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