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 v...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.展开更多
基金funded by Research Start-up Fund of Suqian University,The interdisciplinary Integration and Innovation Project of Suqian University(grant number 2025XKTD 02)Qinglan Project of Jiangsu Province.
文摘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.
