Asymptotics of the heat exchange

Let K be a compact subset in Euclidean space R-m, and let E-K(t) denote the total amount of heat in R-m\K at time t, if K is kept at fixed temperature 1 for all tgreater than or equal to0, and if R-m\K has initial temperature 0. For two disjoint compact subsets K-1 And K-2 we define the heat exchange H-K 1,H- K2 (t)=E-K 1 (t)+E-K 2 (t)-E-K 1boolean ORK 2 (t). We obtain the leading asymptotic behaviour of HK,,K2(t) as t-->0 under mild regularity conditions on K-1 and K-2. (C) 2003 Elsevier Inc. All rights reserved.