Research On The Asymptotic Behavior Of Solutions Of G-Kelvin-Voight Equation

Infinite-dimensional dynamical system,an independent discipline,is widely used.Some partial differential equations,such as those generated in natural science,are the main objects of this system.The study of these developed partial differential equations,on the one hand,effectively promotes us to break through the limitations of inherent conditions,thus opening up new research field;On the other hand,it also provides new ideas and methods for understanding and transforming nature.Asymptotic behavior analysis is the core content of infinite dimensional dynamical system theory,so this thesis studies the asymptotic behavior of g-Kelvin-Voight equation based on infinite dimensional dynamical system.This thesis is mainly composed of five parts.The first two parts briefly describe the development of the infinite-dimensional dynamic system,the rich theoretical results of the g-Kelvin-Voight equation on attractors in recent years and the most basic knowledge used in this thesis.In the third part,we mainly study the global attractor of the g-Kelvin-Voight equation in the space of V_g,we verify the asymptotic compactness of the equation and obtain the bounded absorption set of the equation by using the operator decomposition method,thus proving the existence of the global attractor of the equation.In the fourth part,under the premise of obtaining the global attractor of the g-Kelvin-Voight equation,we obtain that the equation is semigroup differentiable,and then use the Sobolev-Lieb Thirring inequality to estimate the fractal dimension of the equation.In the fifth part,it is proved that in the space of V_g,the exponential attractor of the equation.Mainly use the operator decomposition technique and Lipschitz continuity to obtain the existence of the exponential attractor of the two-dimensional g-Kelvin-Voight equation.