Communications in Analysis and Geometry
Volume 12 (2004)
Asymptotics of the Heat Flow on a Manifold with Smooth Boundary
Pages: 671 – 702
On a compact Riemannian manifold with smooth boundary, we study the solution of the heat equation with smooth initial data and Dirichlet boundary conditions. We compute the whole asymptotic series of the gradient of the solution at any boundary point, and apply these results to the asymptotics of the heat content with homogeneous and inhomogeneous boundary conditions.