On Benjamin-Bona-Mahony equation

In this thesis, the existence and uniqueness of the solution of the Benjamin-Bona-Mahony equation and also a long time behavior of the solution of this equation, wich is known, has been studied at and [13,22,24]. In the introduction part some studies about the Benjamin-Bona-Mahony equation will be given. In the second part, the basis of definitions and theorems of this study will be given. In the third part by using Feado-Galerkin method, the existence and uniqueness of solutions of the problem for Benjamin-Bona-Mahony equationhas been shown [13]. In the fourth part the existence of weak global attractor has been shown at [24]. At the end of the thesis the existence of weak global attractor is shown at . And also the weak global attractor has been shown to be strong global attractor by energy inequality [22] .