Corrector estimates in homogenization of a nonlinear transmission problem for diffusion equations in connected domains

Corrector estimates in homogenization of a nonlinear transmission problem for diffusion equations in connected domains Full article

Journal

Mathematical Methods in the Applied Sciences
ISSN: 0170-4214

Output data

Year: 2020, Volume: 43, Number: 4, Pages: 1838-1856 Pages count : 19 DOI: 10.1002/mma.6007

Tags

bidomain model; corrector estimates; diffusion problem; nonlinear transmission conditions; periodic unfolding technique

Authors

Kovtunenko Victor A. ^1,2 , Reichelt Sina ³ , Zubkova Anna V. ¹

Affiliations

1	Institute for Mathematics and Scientific Computing, Karl-Franzens University of Graz
2	Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences
3	Weierstrass Institute for Applied Analysis and Stochastics, Partial Differential Equations, Berlin, Germany

This paper is devoted to the homogenization of a nonlinear transmission problem stated in a two-phase domain. We consider a system of linear diffusion equations defined in a periodic domain consisting of two disjoint phases that are both connected sets separated by a thin interface. Depending on the field variables, at the interface, nonlinear conditions are imposed to describe interface reactions. In the variational setting of the problem, we prove the homogenization theorem and a bidomain averaged model. The periodic unfolding technique is used to obtain the residual error estimate with a first-order corrector.

Kovtunenko V.A. , Reichelt S. , Zubkova A.V.
Corrector estimates in homogenization of a nonlinear transmission problem for diffusion equations in connected domains
Mathematical Methods in the Applied Sciences. 2020. V.43. N4. P.1838-1856. DOI: 10.1002/mma.6007 WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000496643200001
Scopus:	2-s2.0-85075440284
Elibrary:	43218897
OpenAlex:	W2983019202

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Scopus	6
OpenAlex	8
Elibrary	6
Web of science	6