Pullback Asymptotic Behavior Of Non-classical Diffusion Equations Driven By Colored Noise

In this master’s thesis we mainly study the existence and uniqueness of pullback random attractor of the nonautonomous non-classical diffusion equations with colored noise.It focuses on the following two problems.First,we study the nonautonomous non-classical diffusion equation driven by colored noise on Rn,(?)To begin with,the measurability of multivalued random mapping related to problem(1)is proved,and then a multivalued random dynamic system is defined.Secondly,the existence of the pullback random absorbing set and the pullback asymptotic compactness of the multivalued random dynamic system are proved,thus the existence and uniqueness of the pullback random attractor of problem(1)in H1(Rn)are obtained.Second,we study the nonautonomous non-classical diffusion equation with colored noise and time delay on Rn,(?)Different from the research in the first part,because the influence of time delay is considered in equation(2),a new phase space C([-h,0],H1(Rn))is defined.Similar to the first part,measurable multivalued stochastic dynamic systems are first obtained.Then,by using the energy equation and tail estimate,we prove the pullback asymptotic compactness of the solution in C([-h,0],H1(Rn)),thus proving the existence and uniqueness of the pullback random attractor of problem(2)in C([-h,0],H1(Rn)).