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The heat equation and reflected Brownian motion in time-dependent domains.: II. Singularities of solutions |
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| Authors: | Krzysztof Burdzy Zhen-Qing Chen John Sylvester |
| Institution: | Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, USA |
| Abstract: | We study the space-time Brownian motion and the heat equation in non-cylindrical domains. The paper is mostly devoted to singularities of the heat equation near rough points of the boundary. Two types of singularities are identified—heat atoms and heat singularities. A number of explicit geometric conditions are given for the existence of singularities. Other properties of the heat equation solutions are analyzed as well. |
| Keywords: | Brownian motion Space-time Brownian motion Heat equation Parabolic equations Neumann boundary conditions Non-cylindrical domains |
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