Time-isolated Singularities of Temperatures

Journal of the Australian Mathematical Society

Neil A. Watson¹ 

关键词: primary 35K05;    35B30;    35B60;    35C05;    31B35;   

DOI  :  10.1017/S1446788700035977

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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 ∩ (Rn × ]0. ∞[), for a suitable open set D, with singularities at compact subset K of Rn × {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∖K.

【 授权许可】

Unknown