The Study Of Attractor For A Type Of Shallow Equations With Dissipation

In this paper ,C-H equation with dissipation are studied mostly relying on some prior estimation ,Kato theory and compactness method. There are three charters in the paper:The first sections, we introduce the background and summarize the main results about them.The second sections, we firstly consider the initial boundary value problem of the C-H equation with strong dissipation on the periodical boundary. The existence of the global solution and the exponential attractor is obtained.Next, The existence of the solution on the interval [0,1] and the attractor are obtained.Finally, we consider the initial boundary value problem of the generalized C-H equation on the total domain. The existence of the global solution are proved. At the same time ,the Blow-up phenomena is founded under special contions.