Existence results for L1 data of some quasi-linear parabolic problems with a quadratic gradient term and source

In this paper we deal with a Cauchy-Dirichlet quasilinear parabolic problem containing a gradient lower order term; namely, u(t) - Deltau + \u\(2gamma-2)u\delu\(2) = \u\(p-2)u. We prove that if p greater than or equal to 1, gamma greater than or equal to 1/2 and p < 2gamma + 2, then there exists a global weak solution for all initial data in L-1 (Ohm). We also see that there exists a non-negative solution if the initial datum is non-negative.