Uniform attractors for a weakly damped wave equation with sup-cubic nonlinearity

Convergence of Non-autonomous Attractors for Subquintic Weakly Damped Wave Equation

“…for which we prove the results on the existence and asymptotic smoothness of Shatah-Struwe solutions, derive the asymptotic smoothing estimates and obtain the result on the upper-semicontinuous convergence of attractors. Thus we extend and complete the previous results in [27] where only the autonomous case was considered, and in [30,31] where the nonlinearity was only in the autonomous term. We stress some key difficulties and achievements of our work.…”

“…Mei, Xiong, and Sun [31] obtained the existence of the pullback attractor for the problem governed by the equation u tt + u t − u + f (u) = g(t), (1.4) for the subquintic case on the space domain given by whole R 3 in the so called locally uniform spaces. Mei and Sun [30] obtained the existence of the uniform attractor for non a translation compact forcing term for the problem governed by (1.4) with subquintic f . Finally, Chang, Li, Sun, and Zelik [12] considered the problem of the form…”

Attractors for semilinear wave equations with localized damping and external forces

“…We refer the reader to, e.g. [8,10,19,23,24,31] for some recent works on attractors for wave equations with cubic and quintic nonlinearities.…”

Kolmogorov $\varepsilon$-entropy of the uniform attractor for a wave equation

“…With the progress on the wave equations obtained in recent years, there are some results show that one can still obtain the existence and structure of the strong uniform attractor for the system with more general external forces which are not translation compact, see e.g. [19,21,23,28]. Meanwhile, based on the recent extension of the Strichartz type estimates for the bounded domains in [2,4], the attractor theory has been developed for semilinear wave equations concerning sup-cubic nonlinearities in both autonomous and non-autonomous cases, see [17,20,21,23].…”