2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223448Under fairly general assumptions, we prove that every compact invariant subset $\mathcal I$ of the semiflow generated by the semilinear damped wave equation εu_{tt}+u_t+β(x)u-\sum_{ij}(a_{ij} (x)u_{x_j})_{x_i}&=f(x,u),&& (t,x)\in[0,+\infty[\timesΩ, u&=0,&&(t,x)\in[0,+\infty[\times\partialΩin $H^1_0(Ω)\times L^2(Ω)$ is in fact bounded in $D(\mathbf A)\times H^1_0(Ω)$. Here $Ω$ is an arbitrary, possibly unbounded, domain in $\R^3$, $\mathbf A u=β(x)u-\sum_{ij}(a_{ij}(x)u_{x_j})_{x_i}$ is a positive selfadjoint elliptic operator and $f(x,u)$ is a nonlinearity of critical growth. The nonlinearity $f(x,u)$ needs not to satisfy any dissipativeness assumption and the invariant subset $\mathcal I$ needs not to be an an attractor.23 pagesAnalysis of PDEsDynamical Systems35L70; 35B40; 35B65text