Variational Problems on Domains with Inclusions Homogenization Through Gamma-Convergence

Title:	Variational Problems on Domains with Inclusions Homogenization Through Gamma-Convergence
Author:	Gyrya, Vitaliy
Description:	Consider a composite material consisting of a periodic (with a period d) collection of alternating flat plates (laminates) with two different values of thermal conductivity. Suppose that thermal conductivity is equal to 1 in the first set of plates and it is equal to c in the second set of plates. We focus on finding the effective conductivity of the laminated composite when the parameter c is large and the parameter d is small. This problem can be solved by determining the partial differential equation governing the homogenized temperature distribution. Rather than go this route, we choose to formulate the problem in a variational form. Then the conductivity of a composite for the given values c and d can be determined by minimizing an appropriate energy functional. We use the theory of Γ-convergence to find the asymptotic limits of both minimizers and their respective minimum energy values as (c-1,d) approaches (0,0). We show that these limits are independent of the direction in which (c-1,d) approaches (0,0) in the parameter space. Further, we show that the minimum energy values do not exceed the minimum value of the limiting energy functional.
Permanent Link:	http://rave.ohiolink.edu/etdc/view?acc_num=akron1121462160 http://hdl.handle.net/2374.OX/3635
Date:	2005

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