Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


akron1121462160.pdf (302.24 KB)

ETD Abstract Container

Abstract Header

Variational Problems on Domains with Inclusions Homogenization Through Gamma-Convergence

Gyrya, Vitaliy
http://rave.ohiolink.edu/etdc/view?acc_num=akron1121462160

Abstract Details

2005, Master of Science, University of Akron, Applied Mathematics.
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.
Dmitry Golovaty (Advisor)
71 p.
Mathematics

Recommended Citations

Citations

  • Gyrya, V. (2005). Variational Problems on Domains with Inclusions Homogenization Through Gamma-Convergence [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1121462160

    APA Style (7th edition)

  • Gyrya, Vitaliy. Variational Problems on Domains with Inclusions Homogenization Through Gamma-Convergence. 2005. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1121462160.

    MLA Style (8th edition)

  • Gyrya, Vitaliy. "Variational Problems on Domains with Inclusions Homogenization Through Gamma-Convergence." Master's thesis, University of Akron, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=akron1121462160

    Chicago Manual of Style (17th edition)

akron1121462160
585
© 2005, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.