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The paper investigates the existence of global attractors for a few classes of multi-valued operators. We establish some criteria and give their applications to a strongly damped wave equation with fully supercritical nonlinearities and without the uniqueness of solutions. Moreover, the geometrical structure of the global attractors of the corresponding multi-valued operators is shown. [ABSTRACT FROM AUTHOR]

The paper investigates the upper semicontinuity of global attractors A α of a family of semilinear wave equations with gentle dissipation: u t t − △ u + γ ( − △ ) α u t + f ( u ) = g ( x ) , with α ∈ ( 0 , 1 ∕ 2 ) . It is a continuation of researches in Yang et al. (2016), where the existence of global attractors of the equations has been established. We further show that for any neighborhood U of A α 0 , α 0 ∈ ( 0 , 1 ∕ 2 ) , A α ⊂ U when 0 < α − α 0 ≪ 1 . [ABSTRACT FROM AUTHOR]

The paper studies the longtime dynamics of the Kirchhoff equation with strong damping and critical nonlinearity on R N : u t t − Δ u t − M ( ‖ ∇ u ‖ 2 ) Δ u + u t + g ( x , u ) = f ( x ) . We establish the well-posedness, the existence of the global and exponential attractors in natural energy space H = H 1 ( R N ) × L 2 ( R N ) in critical nonlinearity case. These results improve not only the recent ones achieved by Yang (2007) [32] , but also ones achieved by Conti, Pata and Squassina (2005) [9] to some extent. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: The paper studies the existence of global strong attractor for the Kirchhoff type equations with strong nonlinear damping and supercritical nonlinearity . It proves that in strictly positive stiffness factors and supercritical nonlinearity case, there exists a global finite-dimensional attractor in the natural energy space endowed with strong topology (rather than partially strong topology). The result extends the recent one achieved by Chueshov (2012). [Copyright &y& Elsevier]

Abstract: The paper studies the longtime dynamics of the damped Boussinesq equation . First, the existence of global solutions to the initial boundary value problem of the equation is obtained provided that the growth exponent of , say , is either non-supercritical (subcritical and critical) or supercritical, especially, the stability of solutions is established when is non-supercritical. Second, the existence of a global attractor and an exponential attractor for the related solution semigroup are respectively established in the non-supercritical case. [Copyright &y& Elsevier]

Abstract: This paper studies the longtime behavior of solutions to the elastic waveguide model in . It proves that when the space dimension , under rather mild conditions on and the related solution semigroup possesses in phase space with low regularity , with , a global attractor which is connected. [Copyright &y& Elsevier]

Abstract: The paper studies the existence of the finite-dimensional global attractors and exponential attractors for the dynamical system associated with the Kirchhoff type equation with a strong dissipation . It proves that the above mentioned dynamical system possesses a global attractor which has finite fractal dimension and an exponential attractor. For application, the fact shows that for the concerned viscoelastic flow the permanent regime (global attractor) can be observed when the excitation starts from any bounded set in phase space, and the dimension of the attractor, that is, the number of degree of freedom of the turbulent phenomenon and thus the level of complexity concerning the flow, is finite. [Copyright &y& Elsevier]

Abstract: The paper studies the longtime behavior of solutions to the initial boundary value problem (IBVP) for a nonlinear wave equation arising in an elastic waveguide model . It proves that when the space dimension , under rather mild conditions the dynamical system associated with the above-mentioned IBVP possesses a global attractor which is connected and has finite fractal and Hausdorff dimension. [Copyright &y& Elsevier]