  Convergence to a single steady state is shown for non-negative and radially
symmetric solutions to a diffusive Hamilton-Jacobi equation with homogeneous
Dirichlet boundary conditions, the diffusion being the $p$-Laplacian operator,
$p\ge 2$, and the source term a power of the norm of the gradient of $u$. As a
first step, the radially symmetric and non-increasing stationary solutions are
characterized.
