Homogenization of imperfect transmission problems: the case of weakly converging data. (English) Zbl 1463.35064

Faella, Luisa; Monsurrò, Sara; Perugia, Carmen

Differ. Integral Equ. 31, No. 7-8, 595-620 (2018).

The authors dwell with the homogenization asymptotic behavior of solutions to an elliptic problem with rapidly oscillating coefficients posed in a periodic two-component composite. The special feature is a scaling (in the small parameter) that describes an interfacial contact resistance at the interface. The asymptotic analysis is performed for the case of weakly converging data.

Reviewer: Adrian Muntean (Karlstad)

MSC:

35B27	Homogenization in context of PDEs; PDEs in media with periodic structure
35J25	Boundary value problems for second-order elliptic equations
82B24	Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics

Keywords:

homogenization; elliptic equations; imperfect transmission conditions