Study On The Asymptotic Behavior Of Three Evolution Equations

There is a close relationship between infinite dimensional dynamical systems and science. So, the study about it has an important value.In this dissertation,We introduce the development during these years and mainly consider some relevant problems about attractors in this field.We acquire some results of global attractors ,exponential attractors and asymptotic attractors through studying the asymptotic behaviors of solutions for three kinds of equations.First, we consider the existence of exponential attractor for the non-classical diffusion equation g∈L² (Ω) , f(s) is a smooth function, f(0) = 0If f(s) satisfies the following conditions , global attractor is exist in H₀¹(Ω).We prove the existence of exponential attractor by modifying the condition, and we acquire better results in the second part of dissertation. Second,the other equation is the generalized BBM equationwe consider the asymptotic behavior of the solution ,and prove the existence of global attractor with energy equation method in H_per²(Ω).Finally, we prove the finite dimensional asymptotic attractor for BBM equation under the periodic boundary condition.