LJKDeterministic Models and Algorithms: EDPMOISE Seminar

On Thursday April 24 2014 at 11h00 in waiting for a room

Seminary of Mr Paolo MUSOLINO (Università di Padova)

A quasilinear heat transmission problem in a periodic twophase dilute composite

Summary

We consider a temperature transmission problem for a composite material which fills the ndimensional Euclidean space. The composite has a periodic structure and consists of two materials. In each periodicity cell one material occupies a cavity of size ε, and the second material fills the remaining part of the cell. We assume that the thermal conductivities of the materials depend nonlinearly upon the temperature. We show that for ε small enough the problem has a solution, i.e. a pair of functions which determine the temperature distribution in the two materials. Then we analyze the behavior of such a solution as ε approaches 0 by an approach which is alternative to those of asymptotic analysis. In particular we prove that if n≥3, the temperature can be expanded into a convergent series expansion of powers of ε and that if n=2 the temperature can be expanded into a convergent double series expansion of powers of ε and ε log ε.
