Journal of the Australian Mathematical Society - Series A
Vol. 65 Part 3 (1998)
Time-isolated singularities of temperatures
Neil A. Watson
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 , for a suitable open set D, with singularities at a compact subset K of , 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 .
PDF file size:
© Copyright 1998, Australian Mathematical Society TeXAdel Scientific Publishing