The 3-Dimensional oscillon equation

On a bounded smooth domain Ω ⊂ R 3, we consider the generalized oscillon equation ∂ uu(x,t) + ω(t) ∂ tu(x,t)-μ(t)Δu(x,t) + V 1(u(x,t))=0, x ∈ Ω ⊂ R 3, t ∈ R, with Dirichlet boundary conditions, where ω is a time-dependent damping, μ is a time-dependent squared speed of propagation, and V is a nonlinear potential of critical growth. Under structural assumptions on ω and μ we establish the existence of a pullback global attractor A = A(t) in the sense of [1]. Under additional assumptions on μ, which include the relevant physical cases, we obtain optimal regularity of the pullback global attractor and finite-dimensionality of the kernel sections.