On the Benjamin–Ono equation in the half line

Abstract

We consider the inhomogeneous Dirichlet initial–boundary value problem for the Benjamin–Ono equation formulated on the half line. We study the global in time existence of solutions to the initial–boundary value problem. This work is a continuation of the ones (Hayashi and Kaikina , 2010, 2012 [15,16]) by Hayashi and Kaikina where the global in time existence and the asymptotic behaviour of solutions for large time were considered.