Some Nonlinear Parabolic Problems with Singular Natural Growth Term

In this paper, we study the existence and regularity results for nonlinear parabolic problems with singular natural growth gradient terms {partial derivative u/partial derivative t - Delta(p)u + b(x, t) |del u|(p)/u(theta) = f in Q, u(x, t) = 0 on Gamma, u(x, 0) = 0 in Omega, where Omega is a bounded open subset of R-N, N >= 2, Q is the cylinder Omega x (0, T), T > 0, G the lateral surface partial derivative Omega x (0, T), Delta(p) is the so-called p-Laplace operator, Delta(p)u = div(vertical bar del u vertical bar(p-2)del u) with 2 <= p < N, b is a positive measurable bounded function, 0 < theta < 1, and f belongs to Lebesgue space L-m(Q), m >= 1.