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 APM  Vol.2 No.5 , September 2012
Global Attractor for a Non-Autonomous Beam Equation
Yonghua Ren, Jianwen Zhang*
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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.
Keywords: Global Attractor; Non-Autonomous Beam Equation; Absorbing Set
Cite this paper: Y. Ren and J. Zhang, "Global Attractor for a Non-Autonomous Beam Equation," Advances in Pure Mathematics, Vol. 2 No. 5, 2012, pp. 358-362. doi: 10.4236/apm.2012.25052.
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