Study On The Exact Controllability Of Third-order Dispersion Equations And Inclusions

In this paper,we investigate the controllability of nonlinear third-order dispersion equations and inclusions mainly by the theory of semigroups.The main results are in chapter 2 and chapter 3.The first part is a brief introduction to the research background,proposing the problem and the significance of studying the problem.In chapter 2,a fixed point analysis approach is used to investigate the exact controllability of nonlinear third-order dispersion equation with infinite distributed delay.Without imposing a compactness condition on the semigroup,we give some sufficient conditions for controllability of this system.Chapter 3 is concerned with the controllability of nonlinear third-order dispersion inclusions with infinite delay.Sufficient conditions for controllability are obtained by using a fixed-point theorem for multivalued maps.Particularly,the compactness of the semigroups is not needed in this chapter.