Inertial manifolds for nonlinear viscoelasticity equations

摘要

In this paper, we investigate the dynamical behaviour of the following one-dimensional dispersive viscoelasticity equation:The nonlinear functionis smooth, non-convex, unbounded and satisfies some general conditions of growth. By introducing equivalent norms, based on the Hamiltonian structure of the limit dispersive problem with, we can prove the existence of global absorbing balls, and a global attractor. Depending on the parameters, we make different transformations depending on whetheris positive or negative; the latter case is the most interesting one as the dissipation is not strong enough to dominate dispersion. The semigroupS(t) generated bysatisfies a spectral barrier property, and the existence of inertial manifolds is proved in both cases.