Homogenization of the signorini boundary-value problem in a thick plane junction

We consider a mixed boundary-value problem for the Poisson equation in a plane thick junction Ω_ε that is the union of a domain Ω₀ and a large number of ε-periodically located thin rods. The nonuniform Signorini conditions are given on the vertical sides of the thin rods. The asymptotic analysis of this problem is made as ε → 0, i.e., in the case where the number of thin rods infinitely increases and their thickness tends to zero. With the help of the integral identity method, we prove the convergence theorem and show that the nonuniform Signorini conditions are transformed (as ε → 0) into the limiting variational inequalities in the domain that is filled up with thin rods when passing to the limit. The existence and uniqueness of a solution to this nonstandard limit problem are established. The convergence of the energy integrals is proved as well. Published in Neliniini Kolyvannya, Vol. 12, No. 1, pp. 44–58, January–March, 2009.