Abstract
AbstractWe investigate the heat flow in an open, bounded set D in $$\mathbb {R}^2$$
R
2
with polygonal boundary $$\partial D$$
∂
D
. We suppose that D contains an open, bounded set $$\widetilde{D}$$
D
~
with polygonal boundary $$\partial \widetilde{D}$$
∂
D
~
. The initial condition is the indicator function of $$\widetilde{D}$$
D
~
and we impose a Neumann boundary condition on the edges of $$\partial D$$
∂
D
. We obtain an asymptotic formula for the heat content of $$\widetilde{D}$$
D
~
in D as time $$t\downarrow 0$$
t
↓
0
.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
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