JOURNAL BROWSE
Search
Advanced SearchSearch Tips
GLOBAL ATTRACTOR OF THE WEAKLY DAMPED WAVE EQUATION WITH NONLINEAR BOUNDARY CONDITIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
GLOBAL ATTRACTOR OF THE WEAKLY DAMPED WAVE EQUATION WITH NONLINEAR BOUNDARY CONDITIONS
Zhu, Chaosheng;
  PDF(new window)
 Abstract
In this paper, the main purpose is to study existence of the global attractors for the weakly damped wave equation with nonlinear boundary conditions. To this end, we first show that the existence o a bounded absorbing set by the perturbed energy method. Secondly, we utilize the decomposition of the solution operator to verify the asymptotic compactness.
 Keywords
wave equation;nonlinear boundary conditions;global attractor;
 Language
English
 Cited by
 References
1.
R. B. Anibal, Attractors for parabolic equations with nonlinear boundary conditions, critical exponents, and singular initial data, J. Differential Equations 181 (2002), no. 1, 165-196. crossref(new window)

2.
A. N. Carvalho, S. M. Oliva, A. L. Pereira, and R. B. Anibal, Attractors for parabolic problems with nonlinear boundary conditions, J. Math. Anal. Appl. 207 (1997), no. 2, 409-461. crossref(new window)

3.
G. Chen, Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain, J. Math. Pures Appl. (9) 58 (1979), no. 3, 249-273.

4.
V. Komornik and E. Zuazua, A direct method for the boundary stabilization of the wave equation, J. Math. Pures Appl. (9) 69 (1990), no. 1, 33-54.

5.
I. N. Kostin, Long-time behavior of solutions to a semilinear wave equation with boundary damping, Dynam. Control 11 (2001), no. 4, 371-388. crossref(new window)

6.
J. Lagnese, Decay of solutions of wave equations in a bounded region with boundary dissipation, J. Differential Equations 50 (1983), no. 2, 163-182. crossref(new window)

7.
I. Lasiecka, Stabilization of wave and plate-like equations with nonlinear dissipation on the boundary, J. Differential Equations 79 (1989), no. 2, 340-381. crossref(new window)

8.
I. Lasiecka and R. Triggiani, Uniform Stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions, Appl. Math. Optim. 25 (1992), no. 2, 189-224. crossref(new window)

9.
J. E. Munoz Rivera, Smoothness effect and decay on a class of nonlinear evolution equation, Ann. Fac. Sci. Toulouse Math. (6) 1 (1992), no. 2, 237-260. crossref(new window)

10.
D. Tataru, Uniform decay rates and attractors for evolution PDE's with boundary dissipation, J. Differential Equations 121 (1995), no. 1, 1-27. crossref(new window)

11.
R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, New York, Springer, 1988.

12.
E. Zuazua, Stability and decay for a class of nonlinear hyperbolic problems, Asymptotic Anal. 1 (1988), no. 2, 161-185.