Asymptotics of the heat exchange

Abstract

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 t⩾0, 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, K 2 ( t)= E K 1 ( t)+ E K 2 ( t)− E K 1∪ K 2 ( t). We obtain the leading asymptotic behaviour of H K 1, K 2 ( t) as t→0 under mild regularity conditions on K 1 and K 2.