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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]

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 longtime behavior of the Kirchhoff type equation with strong damping on . It shows that the related continuous semigroup possesses a global attractor which is connected and has finite fractal and Hausdorff dimension. [Copyright &y& Elsevier]