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 'U IND.TT' −Δu−Δ'U IND.TT' +'Δ POT.2'u−Δ'U IND.T' − 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.