Decay estimates for a viscous Hamilton-Jacobi equation with homogenious Dirichlet boundary conditions

Said Benachour (1) , Simona Dabuleanu-Hapca (2) , Philippe Laurençot (3)

1 IECN - Institut Élie Cartan de Nancy
2 SIMBIOS - SIMBIOS centre
3 MIP - Mathématiques pour l'Industrie et la Physique

Global classical solutions to the viscous Hamilton-Jacobi equation with homogenious Dirichlet boundary conditions are shown to converge to zero at the same speed as the linear heat semigroup when p > 1. For p = 1, an exponential decay to zero is also obtained in one space dimension but the rate depends on a and differs from that of the linear heat equation. Finally, if 0 < p < 1 and a < 0, finite time extinction occurs for non-negative solutions.

Mots clés: Viscous Hamilton-Jacobi equations; Dirichlet boundary condition; large time behaviour; Heat semigroup.; Heat semigroup

Domaines: Equations aux dérivées partielles [math.AP]

Said Benachour, Simona Dabuleanu-Hapca, Philippe Laurençot. Decay estimates for a viscous Hamilton-Jacobi equation with homogenious Dirichlet boundary conditions. Asymptotic Analysis, 2007, 51 (3-4), pp.209-229. ⟨10.48550/arXiv.math/0609332⟩. ⟨hal-00093133⟩