Homogenization of the parabolic Signorini boundary-value problem in a thick junction of type 3:2:1

• Main Authors: Mel'nyk T.A., Nakvasiuk Yu.A.
• Format: Article
• Language: English
• Published: Vasyl Stefanyk Precarpathian National University 2012-06-01
• Series: Karpatsʹkì Matematičnì Publìkacìï
• Online Access: http://journals.pu.if.ua/index.php/cmp/article/view/97/86

We consider a parabolic Signorini boundary-value problemin a thick junction $Omega_{varepsilon}$ which is the union ofa domain $Omega_0$ and a large number of $varepsilon-$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$varepsilono0,$ i.e., when the number of the thin cylindersinfinitely increases and their thickness tends to zero. With the help of theintegral identity method we prove a convergence theorem and showthat the Signorini conditions are transformed (as $varepsilono0)$ in differential inequalitiesin the region that is filled up by the thin cylinders.