J. Austral. Math. Soc. (Series A) 65 (1999), 416–428 TIME-ISOLATED SINGULARITIES OF TEMPERATURES

We study singularities of solutions of the heat equation, that are not necessarily isolated but occur only in a single characteristic hyperplane. We prove a decomposition theorem for certain solutions on DC D D \.R n]0;1[/, for a suitable open set D, with singularities at a compact subset K of R nf0g, in terms of Gauss-Weierstrass integrals. We use this to prove a representation theorem for certain solutions on DC, with singularities at K, as the sums of potentials and Dirichlet solutions. We also give conditions under which K is removable for solutions on DnK