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 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.
Share and Cite:
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.
Conflicts of Interest
The authors declare no conflicts of interest.
References
[1]
|
S. Woinowsky-Krieger, “The Effect of Axial Force on the Vibration of Hinged Bars,” Journal of Applied Mechanics, Vol. 17, 1950, pp. 35-36.
|
[2]
|
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
|
[3]
|
R. Temam, “Infinite Dimensional Dynamical System in Mechanics and Physical,” 2nd Edition, Spring-Verlag, Nork York, 1997.
|
[4]
|
Q. Z. Ma and C. K. Zhong, “Existence of Strong Global Attractors for Hyperbolic Equation with Linear Memory,” Applied Mathematics and Computation, Vol. 157, No. 1, 2004, pp. 745-758. doi:10.1016/j.amc.2003.08.080
|
[5]
|
Q. Z. Ma and C. K. Zhong, “Global Attractors of strong Solutions for Nonclassical Diffusion Equation,” Journal of Lanzhou University, Vol. 40, 2004, pp. 7-9.
|