Asymptotics of solutions of the heat equation in cones and dihedra under minimal assumptions on the boundary
1 Institute of Mathematics, Linköping University, Linköping, SE-58183, Sweden
2 Institute of Mathematics, University of Rostock, Rostock, D-18051, Germany
Boundary Value Problems 2012, 2012:142 doi:10.1186/1687-2770-2012-142Published: 3 December 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 . Here the right-hand side f of the heat equation is assumed to be an element of a weighted -space. The authors describe the behavior of the solution near the -dimensional edge of the domain.