Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent

2010/03/24 by Azer Khanmamedov, Khanmamedov, Azer
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #math.AP #math.DS #msc:35B41 #msc:35L05 #msc:35L75

paper · pdf · doi:10.48550/arxiv.1003.4760

arxiv created 2012/02/27 · arxiv updated 2012/02/28

Abstract

In this paper the long time behaviour of the solutions of 3-D strongly damped wave equation is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H₀¹(Ω)× L₂(Ω) and then it is proved that this global attractor is a bounded subset of H²(Ω)× H²(Ω) and also a global attractor in H²(Ω)∩ H₀¹(Ω)× H₀¹(Ω).

Related

• Well-posedness and global attractor for wave equation with displacement dependent damping and super-cubic nonlinearity
• Strongly damped wave equation with exponential nonlinearities
• Well-posedness and global attractor for wave equation with nonlinear damping and super-cubic nonlinearity
• Finite-dimensional attractors for the quasi-linear strongly-damped wave equation
• On the regularity of global attractors