On certain nonlinear parabolic equations with singular diffusion and data in L1

An existence result is established for a class of nonlinear parabolic equations having a coercive diffusion matrix blowing-up for a finite value of the unknown, a second hand f is an element of L-1(Q), and an initial data u(o) is an element of L-1(Omega). We develop a technique which relies on the notion of a renormalized solution and an adequate regularization in time for certain truncation functions. Some uniqueness results are also shown under additional hypotheses.