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 ut−Δpu=h(u)f+μinΩ×(0,T),u=0on∂Ω×(0,T),u=u0inΩ×{0}, where Ω is an open bounded subset of RN (N≥2), u0 is a nonnegative integrable function, Δp is the p-Laplace operator, μ is a nonnegative bounded Radon measure on Ω×(0,T) and f is a nonnegative function of L1(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.
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