Research Communication | Open Access
Volume 2019 | Communication ID 311
Volume 2019 | Communication ID 311
| Nonlinear parabolic problem with absorption term and non-regular data |
Mohammed Abdellaoui, Elhoussine Azroul
Received |
Accepted |
Published |
Feb 14, 2019 |
Feb 26, 2019 |
Mar 01, 2019 |
Abstract: We study existence of solutions to a nonlinear parabolic boundary value problem with a general absorption term and a measure as non-regular datum, of the form (b(u)_t -Δ_p u+h(u)=μ in Ω×(0,T), u=0 on ∂Ω×(0,T), (1.1) b(u)=b(u_0 ) in Ω×{0} , where Ω is an open bounded subset of R^N (N≥2), b:R→R is a C^1-increasing function, b(u_0) is an integrable function, Δ_p is the p-Laplace operator, μ is a bounded Radon measure on Ω×(0,T) and h is a continuous function such that h(s)s≥0. Furthermore, we show uniqueness of solutions in presence of a non-increasing h.