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Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 5
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Articles

Saddle-node bifurcations on approximate inertial manifolds for a driven wave equation

Qiongwei HuangSchool of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, 224051P.R. China.View further author information
,
Changfeng XueSchool of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, 224051P.R. China.View further author information
&
Jiashi TangCollege of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082P.R. China.View further author information
Pages 1059-1069 | Received 23 Nov 2014, Accepted 12 May 2015, Published online: 26 Jun 2015

References

  • Giorgi C, Matarazzo G. An existence theorem for a nonlinear evolution equation in viscoelasticity. Ann. Univ. Ferrara Sez. VII (N.S.). 1980;26:113–124.
  • Ikehata R, Matsuyama T, Nakao M. Global solutions to the initial-boundary value problem for the quasilinear visco-elastic wave equation with a perturbation. Funkcialaj Ekva. 1997;40:293–312.
  • Biler P. Asymptotic behaviour of strongly damped nonlinear hyperbolic equations. RAIRO Modél. Math. Anal. Numér. 1989;23:379–384.
  • Temam R. Infinite dimensional dynamical systems in mechanics and physics. Berlin: Springer; 1988.
  • Leung A, Ji J, Chen G. Resonance control for a forced single-degree-of-freedom nonlinear system. Int. J. Bifurcation Chaos. 2004;14:1423–1429.
  • Tang J, Zhao M, Han F, et al. Saddle-node bifurcation and its control of Burgers-KdV equation. Mod. Phys. Lett. B. 2010;24:567–574.
  • Pata V, Squassina M. On the strongly damped wave equation. Commun. Math. Phys. 2005;253:511–533.
  • Chen F, Guo B, Wang P. Long time behavior of strongly damped nonlinear wave equations. J. Differ. Equ. 1998;147:231–241.
  • Yang X, Chen L. Bifurcation and chaos of an axially accelerating viscoelastic beam. Chaos Soliton. Fract. 2005;23:249–258.
  • Kakantarov V, Zelik S. Finite-dimensional attractors for the quasi-linear strongly-damped wave equation. J. Differ. Equ. 2009;247:1120–1155.
  • Liu Z, Xu Z. A new method of studying the dynamical of the sine-Gordon equation. Phys. Lett. A. 1995;204:343–346.
  • Liu Z, Xu Z, Huang D. Homoclinic orbit of ODE on GAIM of the Sine-Gordon equation. Phys. Lett. A. 1999;258:249–252.

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