A nonlinear parabolic problem with singular terms and nonregular data

We study existence of nonnegative solutions to a nonlinear parabolic boundary value problem with a general singular lower order term and a nonnegative measure as nonhomogeneous datum, of the form {u(t) - Delta(u)(p) = h (u) f + mu in Omega x (0,T), u = 0 on partial derivative Omega x (0,T), u = u(0) in Omega x {0}, where Omega is an open bounded subset of R-N (N >= 2), up is a nonnegative integrable function, Delta(p) is the p-Laplace operator, mu is a nonnegative bounded Radon measure on Omega x (0, T) and f is a nonnegative function of L-1 ( Omega x (0, T)). The term h is a positive continuous function possibly blowing up at the origin. Furthermore, we show uniqueness of finite energy solutions in presence of a nonincreasing h. (C) 2019 Elsevier Ltd. All rights reserved.