Refined Asymptotics for the Infinite Heat Equation with Homogeneous Dirichlet Boundary Conditions

Philippe Laurençot, Christian Stinner
2010 Communications in Partial Differential Equations  
The nonnegative viscosity solutions to the infinite heat equation with homogeneous Dirichlet boundary conditions are shown to converge as time increases to infinity to a uniquely determined limit after a suitable time rescaling. The proof relies on the half-relaxed limits technique as well as interior positivity estimates and boundary estimates. The expansion of the support is also studied.
doi:10.1080/03605302.2010.498493 fatcat:7qnvy3coqvctpidisvcdlwycgu