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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 $D\backslash K$.

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© Copyright 1998, Australian Mathematical Society
TeXAdel Scientific Publishing
1998-09-18