Sharp Decay Estimates and Vanishing Viscosity for Diffusive Hamilton-Jacobi Equations

Benachour, Said; Ben-Artzi, Matania; Laurençot, Philippe

Sharp Decay Estimates and Vanishing Viscosity for Diffusive Hamilton-Jacobi Equations

Authors

Benachour, Said

Ben-Artzi, Matania

Laurençot, Philippe

Description

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.
20 pages