Abstract
We study the heat flow from an open, bounded set D in mathbb {R}^{2} with a polygonal boundary ∂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 ∂D. We calculate the heat content of D in mathbb {R}^{2} at t up to an exponentially small remainder as t↓ 0.
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