A global attractor for the elastic waveguide model in RN

This paper studies the longtime behavior of solutions to the elastic waveguide model in RN:utt−Δu−Δutt+Δ2u−Δut+ut+u−Δg(x,u)=f(x). It proves that when the space dimension N≤5N≤5, under rather mild conditions on gg and ff the related solution semigroup possesses in phase space with low regularity Xδ=(Ḣ−2∩H1+δ)×(Ḣ−2∩Hδ), with 0<δ≤10<δ≤1, a global attractor which is connected.