Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent

The paper is devoted to study of the longtime behavior of solutions of a damped semilinear wave equation in a bounded smooth domain of R³ with the nonautonomous external forces and with the critical cubic growth rate of the nonlinearity. In contrast to the previous papers, we prove the dissipativity of this equation in higher energy spaces E^α, 0<α≤ 1, without the usage of the dissipation integral (which is infinite in our case).