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 Научная публикация

Журнал

Mathematical Methods in the Applied Sciences
ISSN: 0170-4214

Вых. Данные

Год: 2020, Том: 43, Номер: 4, Страницы: 1838-1856 Страниц : 19 DOI: 10.1002/mma.6007

Ключевые слова

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

Авторы

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

Организации

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
РИНЦ:	43218897
OpenAlex:	W2983019202

БД	Цитирований
Scopus	6
OpenAlex	8
РИНЦ	6
Web of science	6