A nonlinear parabolic problem with singular terms and nonregular data. (May 2020) - Oliva, Francescantonio; Petitta, Francesco
Abstract: 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 − Δ p u = h ( u ) f + μ in Ω × ( 0, T ), u = 0 on ∂ Ω × ( 0, T ), u = u 0 in Ω × { 0 }, where Ω is an open bounded subset of R N ( N ≥ 2 ), u 0 is a nonnegative integrable function, Δ p is the p -Laplace operator, μ is a nonnegative bounded Radon measure on Ω × ( 0, T ) and f is a nonnegative function of L 1 ( Ω × ( 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 .