Global attractor for a wave model with nonlocal nonlinear damping

Abstract

This paper investigates the well-posedness and long-time dynamics of a wave model with nonlocal nonlinear damping: utt−Δu+σ(‖∇u‖2)g(ut)+f(u)=h(x). For a new exponent p⁎=6γγ+1(≥3), where γ∈[1,5) is the growth index of the nonlinear damping term g(ut), it shows that, as the growth exponent p of the nonlinearity f(u) satisfies 2≤p≤p⁎, the problem is well-posed and has a global attractor in the natural energy space H=H01(Ω)×L2(Ω).