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arXiv · 2210.06834

Heat flow in polygons with reflecting edges

Sam Farrington·Katie Gittins
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Abstract

We investigate the heat flow in an open, bounded set $D$ in $\mathbb{R}^2$ with polygonal boundary $\partial D$. We suppose that $D$ contains an open, bounded set $\widetilde{D}$ with polygonal boundary $\partial \widetilde{D}$. The initial condition is the indicator function of $\widetilde{D}$ and we impose a Neumann boundary condition on the edges of $\partial D$. We obtain an asymptotic formula for the heat content of $\widetilde{D}$ in $D$ as time $t\downarrow 0$.

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Sam Farrington, Katie Gittins. 2022-10-13. Heat flow in polygons with reflecting edges. https://arxiv.org/abs/2210.06834

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