Viscosity solutions to a parabolic inhomogeneous equation associated with infinity Laplacian

We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and singular parabolic inhomogeneous equation of the form $u_t - \Delta _\infty ^N u = f$ , where . N. denotes the so-called normalized infinity Laplacian given by .N.u=1|Du|2.D2uDu,Du..