Sharp Decay Estimates and Vanishing Viscosity for Diffusive   Hamilton-Jacobi Equations
  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. 
Said Benachour (IECN), Matania Ben-Artzi, Philippe Lauren\c{c}ot (MIP)