IJPAM: Volume 2, No. 3 (2002)

HOMOGENIZATION OF HEAT CONDUCTION
EQUATION IN DOMAIN CONTAINING
SMALL SOURCES

Sanja Marušic
Dept. of Mathematics
Faculty of Transport and Traffic Engineering
University of Zagreb
Vukeliceva 4, 10 000 Zagreb, CROATIA
e-mail: [email protected]


Abstract.In this paper we consider the heat equation in a domain containing large number of small heat sources. We study the asymptotic behaviour as the number of sources tends to $\infty $ and their size tends to $0$, using the method of homogenization. The homogenized equation is the same but it has a source term on the right-hand side. The result was proved under weak geometric assumptions (a)-(d).

Received: April 2, 2002

AMS Subject Classification: 35B27, 35B40

Key Words and Phrases: homogenization, heat equation, sources, weak geometric conditions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 2
Issue: 3