Pullback Attractors for a Critical Degenerate Wave Equation with Time-dependent Damping

2019/11/26 by Dandan Li, Li, Dandan, Qingquan Chang +3
Computer Science · Engineering · Mathematics · #35L70 #35L90 #37L30 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Dynamical Systems (math.DS) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1911.11432

openalex publication_date 2019/11/26 · openalex created_date 2019/12/05 · openalex updated_date 2026/07/28

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 ∂_ttu + β(t)∂_tu = Lu(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.

Citations

• Long-time behavior of second order evolution equations with nonlinear damping

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