Homogenization of the parabolic Signorini boundary-value problem in a thick junction of type 3:2:1 - Mel’nyk Т.А.; Nakvasiuk, Yu.A. (Carpathian Mathematical Publications, 2012)
We consider a parabolic Signorini boundary-value problem in a thick junction Ω_ε which is the union of a domain Ω_0 and a large number of ε-periodically situated thin cylinders. The Signorini conditions are given on the lateral surfaces of the cylinders. The asymptotic analysis of this problem is done as ε→0, i.e., when the number of the thin cylinders infinitely increases and their thickness tends to zero. With the help of the integral identity method we prove a convergence theorem and show that the Signorini conditions are transformed (as ε→0) in differential inequalities in the region that is filled up by the thin cylinders.