<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Asymptotic and global dynamics of weak solutions for a damped nonlinear wave equation with a critical growth exponent on the unbounded domain ℝ<italic><sup>n</sup></italic>(<italic>n</italic> ≥ 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.</p></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.

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

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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...

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

Published Online: Dec 02, 2016

Page range: 581 - 602

Received: Sep 17, 2016

Accepted: Nov 29, 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00045

Keywords
Nonlinear wave equation, global attractor, asymptotic compactness, critical exponent, Vitali-type convergence criterion

© 2016 Yuncheng You, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Dec 02, 2016

Page range: 581 - 602

Received: Sep 17, 2016

Accepted: Nov 29, 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00045

KeywordsNonlinear wave equation, global attractor, asymptotic compactness, critical exponent, Vitali-type convergence criterion

© 2016 Yuncheng You, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Nonlinear wave equation, global attractor, asymptotic compactness, critical exponent, Vitali-type convergence criterion