Pullback attractors for a critical degenerate wave equation with time-dependent damping. (February 2022)

• Record Type: Journal Article
• Authors: Li, Dandan; Chang, Qingquan; Sun, Chunyou
• Is Part Of: Nonlinear analysis. Volume 63(2022)
• Publication Date: 2022-02
• Subjects: Semilinear degenerate damped hyperbolic equation -- Time-dependent damping term -- Critical growth restriction -- Pullback attractor; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103421
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The aim of this paper is to analyze the long-time dynamical behavior of the solution for a degenerate wave equation with time-dependent damping term ∂ t t u + β ( t ) ∂ t u = L u ( x, t ) + f ( u ) on a bounded domain Ω ⊂ R N with Dirichlet boundary conditions. Under some restrictions on β ( t ) and critical growth restrictions on the nonlinear term f, we will prove the local and global well-posedness of the solution and derive the existence of a pullback attractor for the process associated with the degenerate damped hyperbolic problem.