Attractors for damped quintic wave equations in bounded domains

2013/09/24 by Varga Kalantarov, Kalantarov, Varga, Anton Savostianov +3 · 3 citations
Mathematics · #35B40 #35B45 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35B45

paper · pdf · doi:10.48550/arxiv.1309.6272

arxiv created 2013/09/24 · arxiv updated 2013/09/25

Abstract

The dissipative wave equation with a critical quintic nonlinearity in smooth bounded three dimensional domain is considered. Based on the recent extension of the Strichartz estimates to the case of bounded domains, the existence of a compact global attractor for the solution semigroup of this equation is established. Moreover, the smoothness of the obtained attractor is also shown.

Cited by

• The Quintic Wave Equation with Kelvin-Voigt Damping: Strichartz estimates, Well-posedness and Global Stabilization
• Stabilizing Energy-Critical Wave Equation to a Finite Dimensional Attractor via Nonlinear Damping
• Well-posedness and global attractor for wave equation with displacement dependent damping and super-cubic nonlinearity

Related

• Recent progress in attractors for quintic wave equations
• Strong attractors for weakly damped quintic wave equation in bounded domains
• Dynamics of the quintic wave equation with nonlocal weak damping
• Strichartz estimates and smooth attractors for a sub-quintic wave equation with fractional damping in bounded domains
• Uniform attractors for measure-driven quintic wave equation with\n periodic boundary conditions