Global Attractors For Two Kinds Of Nonlinear Evolution Equations

Using nonlinear evolution equations to describe and study the nonlinear problems,which depends on continuous time in the field of physics,biology and engineering technology,etc.,has been an important research direction in the field of nonlinear partial differential equations.In this paper,we mainly analyze the global existence and asymptotic behavior of two kinds of nonlinear evolution equations.The details of the full text is as follows:The first chapter briefly states the development history of the research and the main work in this paper,and at the same time the main results are obtained.The second chapter lists some basic concepts,basic lemmas and inequalities used in this paper.In the third chapter,we investigate a class of generalized nonlinear Kirchhoff-Sine-Gordon equation.Firstly,the existence theorem of solutions is given by some research conclusions;Secondly,by a priori estimate method,the existence of the boundary absorbing set is ob-tained;Lastly,by the suitable decomposition of the semigroup,we study the existence of the global attractors for the equation in the strong topology space.In the fourth chapter,we investigate plate equations with memory and nonlocal.Firstly,the existence theorem of solutions is given by some research conclusions;Secondly,by a priori estimate method and some common inequality,the existence of the boundary absorbing set is obtained;Lastly,by using sobolev compact embedding and contraction function,the asymp-totic compactness of semigroups is proved.Thus,we get the existence of global attractor of the system.