Global Attractor for a Non-Autonomous Beam Equation

Abstract

This work studies the global attractor for the process generated by a non-autonomous beam equation u tt +△ 2 u+ηu t -[β(t)+M(∫ Ω |▽u(x,t)| 2 dx)] △u+g(u, t)=f (x,t) Based on a time-uniform priori estimate method, we first in the space H 0 2 (Ω) × L 2 (Ω) establish a time-uniform priori estimate of the solution u to the equation, and conclude the existence of bounded absorbing set. When the external term f (x,t) is time-periodic, the continuous semigroup of solution is proved to possess a global attractor.