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+μinΩ×(0,T),u=0on∂Ω×(0,T),u=u 0 inΩ×{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.
A nonlinear parabolic problem with singular terms and nonregular data / Oliva, F.; Petitta, F.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 194:(2020), p. 111472. [10.1016/j.na.2019.02.025]
A nonlinear parabolic problem with singular terms and nonregular data
Oliva F.;
2020
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+μinΩ×(0,T),u=0on∂Ω×(0,T),u=u 0 inΩ×{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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
