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

M. Sango¹

¹ Department of Mathematics Vista University Private Bag X1311, Silverton 0127 Pretoria, South Africa

Colloquium Mathematicum, Tome 95 (2003) no. 1, pp. 91-115.

Résumé

We study the initial boundary value problem for the system of thermoelasticity in a sequence of perforated cylindrical domains $Q_T^{(s)}$, $s=1,2,\dots$ We prove that as $s\to \mathrm{\infty }$, 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 $Q_T^{(s)}$. We give an explicit construction of that limit problem.

Détail

DOI : 10.4064/cm95-1-8

Mots-clés : study initial boundary value problem system thermoelasticity sequence perforated cylindrical domains ldots prove rightarrow infty solution problem converges appropriate topologies solution limit initial boundary value problem type containing additional terms which expressed terms quantities related geometry explicit construction limit problem