Refined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions

Details Refined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions Refined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions

2010-04-26

arxiv.org/abs/1004.4418v1

Communications in Partial Differential Equations 36 (2011) 532-546

Mathematics

Analysis of PDEs

Scientific paper

10.1080/03605302.2010.498493

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.

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