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 Ω is a bounded smooth domain in Rn,fis a Cl function and external forcing term g(x,t)∈Lb2(R,L2(Ω)which is translation bounded but not translation compact i.e.||g(x,t)||Ib2(R,I2(Ω))≤M<∞.Secondly,we prove the existence of exponential attractor of the reaction-diffusion equation with the distribution derivative term where Ω is a bounded smooth domain in Rn,/is a Cl function and external forcing term g(x,t)∈ Lb2(R,L2(Ω))which is translation bounded,gi∈Lb2(R,L2(Ω))(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 Ω is a bounded smooth domain in Rn,f is a C2 function and external forcing term g(x,t)∈Lb2(R,L2(Ω))which is translation bounded,gi ∈Lb2(R,L2(Ω))(i=1,2…n),Di =(?)/(?)xi is the distribution derivative.