Summary
Consider the following heat conduction problem. LetD be an open, bounded and connected set in euclidean spaceR 2 with a polygonal boundary. Suppose thatD has temperature 1 at timet=0, while the boundary is kept at temperature 0 for all timet>0. We obtain the asymptotic behaviour for the amount of heat inD at timet up toO(e−q/t) ast→0.
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van den Berg, M., Srisatkunarajah, S. Heat flow and Brownian motion for a region inR 2 with a polygonal boundary. Probab. Th. Rel. Fields 86, 41–52 (1990). https://doi.org/10.1007/BF01207512
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DOI: https://doi.org/10.1007/BF01207512