Well-Posedness of 5th-Order KdV Equation Posed on a Finite Domain with Nonlinear Boundary Values

Abstract

In this article, we investigate the well-posedness of the initial-boundary value problem (I-B-V problem) for the fifth-order KdV equation posed on a finite domain with nonlinear boundary conditions. Firstly, we establish various a priori estimates, including Kato smoothing effects, sharp trace regularity, and nonlinear estimates. Subsequently, we demonstrate that the initial-boundary value problem of the fifth-order KdV equation with quadratic boundary feedbacks is locally well-posed for the appropriately chosen initial value and boundary values.