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

Philippe Laurencot (1) , Christian Stinner (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Fachbereich Mathematik

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.

Mots clés: infinite heat equation; infinity-Laplacian; friendly giant; viscosity solution; half-relaxed limits

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Laurencot, Christian Stinner. Refined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions. Communications in Partial Differential Equations, 2011, 36, pp.532-546. ⟨10.1080/03605302.2010.498493⟩. ⟨hal-00463067⟩