Global attractor for the generalized double dispersion equation. (March 2015) - Yang, Zhijian; Feng, Na; Ma, To Fu
Abstract: The paper studies the existence of global attractor for the generalized double dispersion equation arising in elastic waveguide model u t t − Δ u − Δ u t t + Δ 2 u − Δ u t − Δ g ( 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.