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