Longtime behavior for a nonlinear wave equation arising in elasto‐plastic flow

The paper studies the longtime behavior of solutions to the initial boundary value problem (IBVP) for a nonlinear wave equation arising in elasto‐plastic flow u tt −div{|∇ u | m −1 ∇ u }−λΔ u t +Δ 2 u + g ( u )= f ( x ). It proves that under rather mild conditions, the dynamical system associated with above‐mentioned IBVP possesses a global attractor, which is connected and has finite Hausdorff and fractal dimension in the phase spaces X 1 = H (Ω) × L 2 (Ω) and X =( H 3 (Ω)∩ H (Ω)) × H (Ω), respectively.