Derivation of effective transmission conditions for domains separated by a membrane for different scaling of membrane diffusivity

DOI10.3934/dcdss.2017039zbMath1360.35096OpenAlexW2606247180MaRDI QIDQ524551

Peter Knabner, Maria Neuss-Radu, Markus Gahn

Publication date: 3 May 2017

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2017039

zbMATH Keywords

homogenizationeffective transmission conditionsnon-linear reaction-diffusion systemsthin heterogeneous layerweak and strong two-scale convergence

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)

Related Items (11)

Formal upscaling and numerical validation of unsaturated flow models in fractured porous media ⋮ Effective transmission conditions for reaction–diffusion processes in domains separated by thin channels ⋮ Derivation of Stokes-plate-equations modeling fluid flow interaction with thin porous elastic layers ⋮ Effective interface conditions for processes through thin heterogeneous layers with nonlinear transmission at the microscopic bulk-layer interface ⋮ Interface potential in composites with general imperfect transmission conditions ⋮ Concentration and homogenization in electrical conduction in heterogeneous media involving the Laplace-Beltrami operator ⋮ Cosh gradient systems and tilting ⋮ Correctors and error estimates for reaction-diffusion processes through thin heterogeneous layers in case of homogenized equations with interface diffusion ⋮ Rigorous Upscaling of Unsaturated Flow in Fractured Porous Media ⋮ Singular limit for reactive transport through a thin heterogeneous layer including a nonlinear diffusion coefficient ⋮ Singular Limit for Reactive Diffusive Transport Through an Array of Thin Channels in case of Critical Diffusivity

Cites Work

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• Passing from bulk to bulk-surface evolution in the Allen-Cahn equation
• Multiscale analysis and simulation of a reaction-diffusion problem with transmission conditions
• On the effective interfacial resistance through rough surfaces
• Functional analysis, Sobolev spaces and partial differential equations
• Periodic unfolding and homogenization
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• 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
• Different choices of scaling in homogenization of diffusion and interfacial exchange in a porous medium
• Water Waves Over Periodic Bottoms in Three Dimensions
• Modelling of an underground waste disposal site by upscaling
• MATCHED ASYMPTOTIC EXPANSION METHOD FOR A HOMOGENIZED INTERFACE MODEL
• On Diffusion in a Fractured Medium

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