SHARP DECAY ESTIMATES AND VANISHING VISCOSITY FOR DIFFUSIVE HAMILTON-JACOBI EQUATIONS

Said Benachour (1) , Matania Ben-Artzi (2) , Philippe Laurençot (3)

1 IECN - Institut Élie Cartan de Nancy
2 Insitute of Mathematics
3 MIP - Mathématiques pour l'Industrie et la Physique

Sharp temporal decay estimates are established for the gradient and time derivative of solutions to a viscous Hamilton-Jacobi equation as well the associated Hamilton-Jacobi equation. Special care is given to the dependence of the estimates on the viscosity. The initial condition being only continuous and either bounded or non-negative. The main requirement on the Hamiltonians is that it grows superlinearly or sublinearly at infinity, including in particular H(r) = r^p for r non-negatif and p positif and different from 1.

Mots clés: General initial data

Mots clés: Hamilton-Jacobi equations; Bernbstein estimates; General initial data.

Domaines: Equations aux dérivées partielles [math.AP]

Said Benachour, Matania Ben-Artzi, Philippe Laurençot. SHARP DECAY ESTIMATES AND VANISHING VISCOSITY FOR DIFFUSIVE HAMILTON-JACOBI EQUATIONS. 2008. ⟨hal-00337773⟩