Symmetry group methods for heat kernels
Mark Craddock, A. H. Dooley · Journal of Mathematical Physics · 2001
We apply methods of symmetry groups to heat equations on ↛ with drift terms and to heat equations for Lie groups. In particular, we are able to characterize those functions f for which equations of the form (∂2u/∂x2)+f(x)ux=ut have a point symmetry which takes a constant solution to the fundamental solution. Further, we apply symmetry methods to the heat equation of the ax+b group.