Journal of the Australian Mathematical Society - Series A Vol. 65 Part 3 (1998) Time-isolated singularities of temperatures Neil A. Watson Department of Mathematics and Statistics University of Canterbury Christchurch New Zealand Abstract: 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 $D_+=D\cap({\mathbf R}^n\times ]0,\infty[)$, for a suitable open set D, with singularities at a compact subset K of ${\mathbf R}^n\times\{0\}$, in terms of Gauss-Weierstrass integrals. We use this to prove a representation theorem for certain solutions on D+, with singularities at K, as the sums of potentials and Dirichlet solutions. We also give conditions under which K is removable for solutions on $D\backslash K$. PDF file size: 87K © Copyright 1998, Australian Mathematical Society