The Research On The Existence Of Attractors For A Class Of Reaction-Diffusion Equations

In this master dissertation,we study the long-time behavior of the reaction-diffusion equations based on theory squeezing property,limit condition(C)and asymptotic priori estimate.Firstly,we obtain the existence of exponential attractor of the reaction-diffusion equation where ? is a bounded smooth domain in Rn,fis a Cl function and external forcing term g(x,t)?Lb2(R,L2(?)which is translation bounded but not translation compact i.e.||g(x,t)||Ib2(R,I2(?))?M<?.Secondly,we prove the existence of exponential attractor of the reaction-diffusion equation with the distribution derivative term where ? is a bounded smooth domain in Rn,/is a Cl function and external forcing term g(x,t)? Lb2(R,L2(?))which is translation bounded,gi?Lb2(R,L2(?))(i=1,2…n),Di=(?)/(?)xi is the distribution derivative.Finally,we study the existence of uniform attractor of the reaction-diffusion equation with the distribution derivative term where ? is a bounded smooth domain in Rn,f is a C2 function and external forcing term g(x,t)?Lb2(R,L2(?))which is translation bounded,gi ?Lb2(R,L2(?))(i=1,2…n),Di =(?)/(?)xi is the distribution derivative.