Homogenization of enhancing thin layers

Huang，Zhonggan

2021-05-05

10.1016/j.jde.2021.02.024

JOURNAL OF DIFFERENTIAL EQUATIONS   影响因子和分区

0022-0396

1090-2732

This paper derives an explicit formula for the effective diffusion tensor by using the solutions to some effective cell problems after homogenizing Road effective boundary conditions (EBCs). The concept of Road EBCs was proposed recently by H. Li and X. Wang, and in this paper, we extend the effective conditions on closed curves to those on patterns, especially on the included nodes. We also prove that homogenization process commutes with the derivation of Road EBCs. By analyzing the effective diffusion tensor, we obtain several rules for maximizing its trace with given Road-effective-diffusivity/scale and length/scale in each cell and define a notion of balanced patterns. Moreover, we give an estimate of the trace of the effective diffusion tensor of patterns satisfying some connectedness as Road-effective-diffusivity/scale goes to infinity.

Balanced pattern Effective diffusion tensor Homogenization Road effective boundary condition

SCI

英语

第一

WOS:000627618500010

MATHEMATICS

2-s2.0-85101155483

Scopus

Department of Mathematics,Southern University of Science and Technology,China

Huang，Zhonggan. Homogenization of enhancing thin layers[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2021,282:330-369.

Huang，Zhonggan.(2021).Homogenization of enhancing thin layers.JOURNAL OF DIFFERENTIAL EQUATIONS,282,330-369.

Huang，Zhonggan."Homogenization of enhancing thin layers".JOURNAL OF DIFFERENTIAL EQUATIONS 282(2021):330-369.