论文标题
多边形的热流和反射边缘
Heat flow in polygons with reflecting edges
论文作者
论文摘要
我们在$ \ mathbb {r}^2 $中使用多边形边界$ \ partial d $中的开放，有限的集合$ d $中的热流。我们假设$ d $包含带有多边形边界$ \ partial \ partial \ widetilde {d} $的开放式，有限的$ \ widetilde {d} $。初始条件是$ \ widetilde {d} $的指示函数，我们在$ \ partial d $的边缘施加了neumann边界条件。我们获得了$ \ widetilde {d} $ in $ d $的渐近含量，如$ d $，作为时间$ t \ downarrow 0 $。
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 $t\downarrow 0$.
