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arXiv · 1902.02606

Heat flow from polygons

Michiel van den Berg·Peter Gilkey·Katie Gittins
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Abstract

We study the heat flow from an open, bounded set $D$ in $\R^2$ with a polygonal boundary $\partial D$. The initial condition is the indicator function of $D$. A Dirichlet $0$ boundary condition has been imposed on some but not all of the edges of $\partial D$. We calculate the heat content of $D$ in $\R^2$ at $t$ up to an exponentially small remainder as $t\downarrow 0$.

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Michiel van den Berg, Peter Gilkey, Katie Gittins. 2019-02-07. Heat flow from polygons. https://arxiv.org/abs/1902.02606

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