Dynamics of Partial Differential Equations
Volume 1 (2004)
Global dynamics of nonlinear wave equations with cubic non-monotone damping
Pages: 65 – 86
For nonlinear wave equations with cubic non-monotone damping, it is proved that the weak solutions exist globally and generate a semiflow. The dissipativity of the semiflow is shown by the asymptotic bootstrap method. Then it is shown that the global weak attractor exists.
nonlinear wave equation, non-monotone damping, asymptotic boot-strap method, global weak attractor
2010 Mathematics Subject Classification
Primary 35-xx. Secondary 37-xx.