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Heat flow from polygons

MPS-Authors
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van den Berg,  M.
Max Planck Institute for Mathematics, Max Planck Society;

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Gittins,  Katie
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

van den Berg, M., Gilkey, P., & Gittins, K. (2020). Heat flow from polygons. Potential Analysis, 53(3), 1043-1062. doi:10.1007/s11118-019-09797-5.


Cite as: http://hdl.handle.net/21.11116/0000-0006-9EED-E
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 $t\downarrow 0$.