Effective interface conditions for processes through thin heterogeneous layers with nonlinear transmission at the microscopic bulk-layer interface

DOI10.3934/nhm.2018028zbMath1418.35026OpenAlexW2899521243MaRDI QIDQ2416907

Markus Gahn, Maria Neuss-Radu, Peter Knabner

Publication date: 24 May 2019

Published in: Networks and Heterogeneous Media (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/nhm.2018028

zbMATH Keywords

weak and strong two-scale convergencenonlinear transmission conditionsunfolding and averaging operator for thin heterogeneous layer

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Homogenization for problems in thermodynamics and heat transfer (80M40) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)

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Cites Work

• Unnamed Item
• Unnamed Item
• Derivation of effective transmission conditions for domains separated by a membrane for different scaling of membrane diffusivity
• Functional analysis, Sobolev spaces and partial differential equations
• Asymptotic analysis for domains separated by a thin layer made of periodic vertical beams
• Analysis and upscaling of a reactive transport model in fractured porous media with nonlinear transmission condition
• The periodic unfolding method for perforated domains and Neumann sieve models
• Homogenization of Reaction--Diffusion Processes in a Two-Component Porous Medium with Nonlinear Flux Conditions at the Interface
• Homogenization via unfolding in periodic layer with contact
• Derivation of the Double Porosity Model of Single Phase Flow via Homogenization Theory
• Effective Transmission Conditions for Reaction-Diffusion Processes in Domains Separated by an Interface
• Homogenization and Two-Scale Convergence
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• Modelling of an underground waste disposal site by upscaling
• The Periodic Unfolding Method in Homogenization
• A Homogenized Model of an Underground Waste Repository Including a Disturbed Zone

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