Kovtunenko Victor A, Reichelt Sina, Zubkova Anna V
Institute for Mathematics and Scientific Computing Karl-Franzens University of Graz, NAWI Graz Graz Austria.
Lavrentyev Institute of Hydrodynamics Siberian Division of the Russian Academy of Sciences Novosibirsk Russia.
Math Methods Appl Sci. 2020 Mar 15;43(4):1838-1856. doi: 10.1002/mma.6007. Epub 2019 Nov 15.
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.
本文致力于研究在两相区域中提出的非线性传输问题的均匀化。我们考虑一个线性扩散方程组，该方程组定义在一个由两个不相交相组成的周期域中，这两个相都是由一个薄界面分隔开的连通集。根据场变量，在界面处施加非线性条件来描述界面反应。在该问题的变分设定中，我们证明了均匀化定理和一个双域平均模型。使用周期展开技术来获得带有一阶校正项的残余误差估计。
