Asymptotics of solutions of the heat equation in cones and dihedra under minimal assumptions on the boundary
Vladimir Arkad'evich Kozlov, J. Roßmann · Boundary Value Problems · 2012
In the first part of the paper, the authors obtain the asymptotics of Green's function of the first boundary value problem for the heat equation in an m-dimensional cone K.The second part deals with the first boundary value problem for the heat equation in the domain K × R n-m .Here the right-hand side f of the heat equation is assumed to be an element of a weighted L p,q -space.The authors describe the behavior of the solution near the (n -m)-dimensional edge of the domain.