  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.
