Heat flow and Brownian motion for a region in R2 with a polygonal boundary

M. van den Berg; S. Srisatkunarajah

doi:10.1007/BF01207512

Heat flow and Brownian motion for a region in R² with a polygonal boundary

M. van den Berg, S. Srisatkunarajah

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

42 Citations (Scopus)

Abstract

Consider the following heat conduction problem. Let D be an open, bounded and connected set in euclidean space R² with a polygonal boundary. Suppose that D has temperature 1 at time t=0, while the boundary is kept at temperature 0 for all time t>0. We obtain the asymptotic behaviour for the amount of heat in D at time t up to O(e^-q/t) as t?0. © 1990 Springer-Verlag.

Original language	English
Pages (from-to)	41-52
Number of pages	12
Journal	Probability Theory and Related Fields
Volume	86
Issue number	1
DOIs	https://doi.org/10.1007/BF01207512
Publication status	Published - Mar 1990

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abstract = "Consider the following heat conduction problem. Let D be an open, bounded and connected set in euclidean space R2 with a polygonal boundary. Suppose that D has temperature 1 at time t=0, while the boundary is kept at temperature 0 for all time t>0. We obtain the asymptotic behaviour for the amount of heat in D at time t up to O(e-q/t) as t?0. {\textcopyright} 1990 Springer-Verlag.",

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N2 - Consider the following heat conduction problem. Let D be an open, bounded and connected set in euclidean space R2 with a polygonal boundary. Suppose that D has temperature 1 at time t=0, while the boundary is kept at temperature 0 for all time t>0. We obtain the asymptotic behaviour for the amount of heat in D at time t up to O(e-q/t) as t?0. © 1990 Springer-Verlag.

AB - Consider the following heat conduction problem. Let D be an open, bounded and connected set in euclidean space R2 with a polygonal boundary. Suppose that D has temperature 1 at time t=0, while the boundary is kept at temperature 0 for all time t>0. We obtain the asymptotic behaviour for the amount of heat in D at time t up to O(e-q/t) as t?0. © 1990 Springer-Verlag.

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JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

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ER -

Heat flow and Brownian motion for a region in R² with a polygonal boundary

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