On some parabolic equations involving superlinear singular gradient terms

In this paper we prove existence of nonnegative solutions to parabolic Cauchy-Dirichlet problems with (eventually) singular superlinear gradient terms. The model equation is u(t)-Delta(p)u=g(u)vertical bar del u vertical bar(q) + h(u)f(t,x) in (0,T) x Omega, Where Omega is an open bounded subset of R-N with N > 2, 0 < T < +infinity, 1 < p < N, and q < p is superlinear. The functions g, h are continuous and possibly satisfying g(0) = +infinity and/or h(0) = +infinity, with different rates. Finally, f is nonnegative and it belongs to a suitable Lebesgue space. We investigate the relation among the superlinear threshold of q, the regularity of the initial datum and the forcing term, and the decay rates of g, h at infinity.