Research
Asymptotics of solutions of the heat equation in cones and dihedra under minimal assumptions on the boundary
Author affiliations
1 Institute of Mathematics, Linköping University, Linköping, SE-58183, Sweden
2 Institute of Mathematics, University of Rostock, Rostock, D-18051, Germany
Citation and License
Boundary Value Problems 2012, 2012:142 doi:10.1186/1687-2770-2012-142
Published: 3 December 2012Abstract
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.
