Attractors Of Non-autonomous And Stochastic Parabolic Equations With Delays

This thesis is devoted to the study of the dynamics of non-autonomous and stochastic parabolicpartial differential equations with delays. The uniform, pullback and random attractors which belongto the product space L~2(O)×C([-r, 0]; L~2(O)) are obtained The thesis contains five chapters.Chapter 1 introduces the historical background, status and latest advanced in infinite dimen-sional dynamical system and presents the definitions and existence theories of uniform, pullback andrandom attractors.In chapter 2 we investigate non-autonomous parabolic partial differential equations with delays.The existence of the weak solutions are obtained and the existence of uniform attractors for non-autonomous dynamical system, which is generated by the parabolic partial differential equations withdelays, is also obtained when the external force is translation compact function and the delays aresmall.Chapter 3 proves the existence of pullback attractors for non-autonomous dynamical systemgenerated by the parabolic partial differential equations with delays when the external force isα-translation exponential functions and the delays are small.Chapter 4 is devoted to the study of stochastic parabolic partial differential equations with ad-ditive white noise and delays. The existence of random attractors for random dynamical system isproved when the delays are small.Chapter 5 studies the non-local PDE model for population dynamics with state-selective delaysand almost periodic external forces. The existence of uniform attractors are obtained for the non-autonomous dynamical system generated by the model when the delays are small.