Asymptotics of the Heat Flow on a Manifold with Smooth Boundary

摘要

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.