Classification of general Wentzell boundary conditions for fourth order operators in one space dimension

In this paper we consider a fourth order linear ordinary differential operator in one space dimension. We impose, at each endpoint, one general Wentzell boundary condition as well as one other linear boundary. Our goal is to classify precisely when these operators are symmetric, semibounded and/or quasiaccretive. In particular these results extend the collection of boundary conditions for which the one-dimensional beam equation utt+c2uxxxx=0 is well-posed.