Global Attractors For Hyperbolic Cahn-Hilliard Equations With Viscosity

In this thesis,we consider long-time behavior of the Cahn-Hilliard equations with viscons constant coefficient and coefficient of viscons variation respectively.On the mild conditions of the viscons coeffcient,we establish the well-posedness of the weak solutions.Next taking advantage of the presence of strict Lyapunov function for the energy solutions,we prove the existence of the global attractors of the system.The details are as followIn the first chapter,we introduce some research backgrounds,recent research progress and state the content of this paperIn the second chapter,we state Sobolev space,inequalities and lemmas which will be used in the sequelIn the third chapter,we introduce two-dimensional constant coefficient hyperbolic Cahn-Hilliard equation with inertial term and damping term.Under mild regularity conditions of the nonlinearity,we prove the uniform boundedness of the solutions without considering lower bound condition on the first derivative of the nonlinear term.Then,we establish the asymptotic compactness of the weak solutions.Next,taking advantage of the presence of strict Lyapunov function for the energy solutions,we prove the existence of the global attractor in(H²(?)? H₀¹(?))× L²(?).In the fourth chapter,we deal with one-dimensional variance coefficient hyperbolic Cahn-Hilliard equation with localized internal damping term.On the mild conditions of the viscons coeffcient,we establish the well-posedness of the weak solutions.Next,taking use of the same method as Chapter 3,we prove the existence of the global attractor in(H²(0,1)? H₀¹(0,1))×L²(0,1)In the fifth chapter,we summarize the full text and bring out some expectations.