POLAT, MUSTAFA

Ph. D., Department of Mathematics

Supervisor: Prof. Dr. Okay Celebi

Co-Supervisor: Prof. Dr. Varga Kalantarov

February 1999, 57 pages

In this thesis, we discuss the existence of a finite fractal dimensional attractor for the generalized Benjamin-Bona-Mahony equation of the form

u_t - a D u_t - b D u + Ñ . (F₁(u) , ... , F_n (u)) = h(x), xÎ W , tÎ R ⁺

with the following initial and boundary conditions

u(x,0) = u₀(x), xÎ W

u(x + L_ie_i, t) = u(x,t), u_xi (x + L_ie_i, t) = u_xi (x,t), xÎ G _i, i = 1, ..., n, tÎ R ⁺

Keywords: Global Attractor, Fractal Dimension, Absorbing Set.