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 vi
scosity. 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.
The large time behavior of zero mass solutions to the Cauchy problem for a convection-diffusion equation. We provide conditions on the size and shape of the initial datum such that the large time asymptotics of solutions is given either by the deriva
tive of the Guass-Weierstrass kernel or by a self-similar solution or by a hyperbolic N-wave
The large time behavior of solutions to Cauchy problem for viscous Hamilton-Jacobi equation is classified. The large time asymptotics are given by very singular self-similar solutions on one hand and by self-similar viscosity solutions on the other hand
