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Heat flow and Brownian motion for a region inR 2 with a polygonal boundary
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  • Published: March 1990

Heat flow and Brownian motion for a region inR 2 with a polygonal boundary

  • M. van den Berg1 &
  • S. Srisatkunarajah2 

Probability Theory and Related Fields volume 86, pages 41–52 (1990)Cite this article

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  • 39 Citations

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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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Author information

Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, Riccarton, EH14 4AS, Edinburgh, UK

    M. van den Berg

  2. Department of Mathematics and Statistics, University of Jaffna, Thirunelvely, Jaffna, Sri Lanka

    S. Srisatkunarajah

Authors
  1. M. van den Berg
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  2. S. Srisatkunarajah
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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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  • Received: 10 April 1989

  • Revised: 12 February 1990

  • Issue Date: March 1990

  • DOI: https://doi.org/10.1007/BF01207512

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Keywords

  • Stochastic Process
  • Heat Conduction
  • Brownian Motion
  • Asymptotic Behaviour
  • Heat Flow
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