Degenerate homogeneous parabolic equations associated with the infinity-Laplacian

We prove existence and uniqueness of viscosity solutions to the degenerate parabolic problem $u_t={\mathrm{\Delta }}_{\mathrm{\infty }}^{h}u$ where ${\mathrm{\Delta }}_{\mathrm{\infty }}^h$ is the $h$-homogeneous operator associated with the infinity-Laplacian, ${\mathrm{\Delta }}_{\mathrm{\infty }}^{h}u=\mathrm{\mid }Du{\mathrm{\mid }}^{h-3}<D^{2}uDu,Du>$. We also derive the asymptotic behavior of $u$ for the problem posed in the whole space and for the Dirichlet problem with zero boundary conditions.