Fourth order differential operators with interior degeneracy and generalized Wentzell boundary conditions

Abstract

In this article we consider the fourth-order operators A_1u:= (au′′ )′′ and A_2u:= au′′′′ in divergence and non divergence form, where a: [0, 1] → R+ degenerates in an interior point of the interval. Using the semigroup technique, under suitable assumptions on a, we study the genera-tion property of these operators associated to generalized Wentzell boundary conditions. We prove the well posedness of the corresponding parabolic problems.