A nonlinear parabolic problem with singular terms and nonregular data. (May 2020)

• Record Type: Journal Article
• Authors: Oliva, Francescantonio; Petitta, Francesco
• Is Part Of: Nonlinear analysis. Volume 194(2020)
• Publication Date: 2020-05
• Subjects: 35K10 -- 35K20 -- 35K65 -- 35K67 -- 35R06; Singular parabolic problems -- Existence and uniqueness -- Measure data; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.02.025
• Languages: English
• ISSNs: 0362-546X

Abstract

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 .