TITLE:
Global Attractor for a Non-Autonomous Beam Equation
AUTHORS:
Yonghua Ren, Jianwen Zhang
KEYWORDS:
Global Attractor; Non-Autonomous Beam Equation; Absorbing Set
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.2 No.5,
September
26,
2012
ABSTRACT: This work studies the global attractor for the process generated by a non-autonomous beam equation utt+△2u+ηut-[β(t)+M(∫Ω|▽u(x,t)|2dx)] △u+g(u, t)=f (x,t) Based on a time-uniform priori estimate method, we first in the space H02(Ω) ×L2(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.