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O. F. Ma, S. H. Wang and C. K. Zhong, “Necessary and Sufficient Conditions for the Existence of Global Attractor for Semigroup and Application,” Indiana University Mathematics Journal, Vol. 51, 2002, pp. 529-551.doi.org/10.1512/iumj.2002.51.2255

has been cited by the following article:

• 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.