Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 87, pp. 1-22.

Title: Fourth-order differential operators with interior degeneracy and generalized Wentzell boundary conditions
       
Authors: Alessandro Camasta (Univ. of Bari Aldo Moro, Bari, Italy)
         Genni Fragnelli (Tuscia Univ., Viterbo, Italy)
         
Abstract: 
In this article we consider the fourth-order operators A_<sub>1</sub>u:=(au'')'' and
A<sub>2</sub>u:=au'''' in divergence and non divergence form,
where a:[0,1]\&rar;R<sub>+</sub> degenerates in an interior point of the interval.
Using the semigroup technique, under suitable assumptions on a, we study the
generation property of these operators associated to generalized Wentzell boundary
conditions. We prove the well posedness of the corresponding parabolic problems.

Submitted September 28, 2021. Published December 29, 2022.
Math Subject Classifications: 47D06, 35K65, 47B25, 47N20.
Key Words: Degenerate operators in divergence and non divergence form;
    generalized Wentzell boundary conditions; interior degeneracy.