Global attractor for the generalized double dispersion equation

Abstract

The paper studies the existence of global attractor for the generalized double dispersion equation arising in elastic waveguide model utt−Δu−Δutt+Δ2u−Δut−Δg(u)=f(x). The main result is concerned with nonlinearities g(u) with supercritical growth. In that case we construct a subclass G of the limit solutions and show that it has a weak global attractor. Especially, in non-supercritical case, the weak topology becomes strong, the further regularity of the global attractor is obtained and the exponential attractor is established in natural energy space.