Abstract
The paper studies the long time behavior of solutions to the initial boundary value problem(IBVP) for a class of Kirchhoff models flow .We establish the well-posedness, theexistence of the global attractor in natural energy space
Highlights
In this paper,we are concerned with the existence of global attractor for the following nonlinear plate equation referred to as Kirchhoff models: utt ut ut ( u 2 ) u (1 | u |2 ) p 1u = f (x) in R, (1.1)
Global attractor is a basic concept in the study of the asymptotic behavior of solutions for nonlinear evolution equations with various dissipation
From the physical point of view, the global attractor of the dissipative equation(1.1)represents the permanent regime that can be observed when the excitation starts from any point in natural energy space, and its dimension represents the number of degree of freedom of the related turbulent phenomenon and the level of complexity concerning the flow
Summary
Tokio Matsuyama and Ryo Ikehata[3] proved on global solutions and energy decay for the wave equations of Kirchhoff type with nonlinear damping terms: utt. RN is a bounded domain with smooth boundary , f (x) is an external force term. It shows that the related continuous semigroup S (t) possesses a global attractor which is connected and has finite fractal and Hausdorff dimension. Zhijian Yang and Pengyan Ding[6] studies the longtime dynamics of the Kirchhoff equation with strong damping and critical nonlinearity on R N : utt ut M ( u 2 ) u ut g(x,u) = f (x),.
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