On a nonlinear singular diffusion problem:existence and uniqueness

The singular diffusion equation u_t=(u^?1u_x)_x:arises in many areas of application, e.g. in the central limit approximation to Carleman's model of Boltzman equation, or, in the expansion of a thermalized electron cloud in plasma physics. This paper concerns the existence and uniqueness of solution of a mixed boundary value problem of equation u_t=(u^m=1u_x)_x for ?1 < m ≤0.