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arXiv · 1504.04165

On the heat content of a polygon

Michiel van den Berg·Katie Gittins
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Abstract

Let $D$ be a bounded, connected, open set in Euclidean space $\mathbb{R}^{2}$ with polygonal boundary. Suppose $D$ has initial temperature $1$ and the complement of $D$ has initial temperature $0$. We obtain the asymptotic behaviour of the heat content of $D$ as time $t \downarrow 0$. We then apply this result to compute the heat content of a particular fractal polyhedron as $t \downarrow 0$.

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Michiel van den Berg, Katie Gittins. 2015-04-16. On the heat content of a polygon. https://doi.org/10.1007/s12220-015-9626-2

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