Asymptotic analysis of the initial boundary value problem for the thermoelastic system in a perforated domain

Abstract

Abstract. We study the initial boundary value problem for the system of thermoelasticity in a sequence of perforated cylindrical domains Q (s) T , s = 1, 2, . . . We prove that as s → ∞, the solution of the problem converges in appropriate topologies to the solution of a limit initial boundary value problem of the same type but containing some additional terms which are expressed in terms of quantities related to the geometry of Q (s)T . We give an explicit construction of that limit problem.

Homogenization of stochastic semilinear parabolic equations with non-Lipschitz forcings in domains with fine grained boundaries

“…More information on results obtained in this kind of deterministic problems can be found in, for example, [44] (heat equations in perforated domains by probabilistic means) and [2,16,13,18,51]. Deterministic evolution problems in non-periodically perforated domains have been less studied; we refer to [12,15,59,52] for some results in this direction.…”