Initial-boundary value problem of fifth-order Korteweg-de Vries equation posed on half line with nonlinear boundary values

Abstract

In this paper, we study the initial boundary problem of fifth-order Korteweg-de Vries equation with nonlinear boundary values. First, we establish a so-called sharp boundary trace regularity associated with the linearized fifth-order Korteweg-de Vries equation. Then, aided by the sharp boundary trace regularity, we verify that initial-boundary value problem of fifth-order Korteweg-de Vries equation with nonlinear boundary conditions is locally well-posed when initial and boundary values are properly chosen.

Keywords

• fifth-order korteweg-de vries equation
• initial-boundary value problem
• nonlinear boundary condition
• sharp boundary trace regularity
• local well-posedness
• 35g16
• 35q53