Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term

We study existence and regularity of distributional solutions for possibly degenerate quasi-linear parabolic problems having a first order term which grows quadratically in the gradient. We give sufficient conditions on the data of our problem in order to have distributional solutions. We point out that the assumptions on the data do not guarantee in general the boundedness of the solutions; this means that the coercivity of the principal part of the operator can really degenerate. Moreover, a boundedness result is proved when the assumptions on the data are strengthened.