Global Attractor for Nonlinear Wave Equations with Critical Exponent on Unbounded Domain

Abstract

Asymptotic and global dynamics of weak solutions for a damped nonlinear wave equation with a critical growth exponent on the unbounded domain ℝn(n ≥ 3) is investigated. The existence of a global attractor is proved under typical dissipative condition, which features the proof of asymptotic compactness of the solution semiflow in the energy space with critical nonlinear exponent by means of Vitali-type convergence theorem.

Keywords

• nonlinear wave equation
• global attractor
• asymptotic compactness
• critical exponent
• vitali-type convergence criterion
• primary 35b40
• 35b41
• 35r60
• 37l55
• secondary 60h15