Pullback attractor for a non-autonomous modified SwiftHohenberg equation
This paper is concerned with a non-autonomous modified SwiftHohenberg equation ut+?2u+2?u+au+b|?u|2+u3=g(x,t) u t + ? 2 u + 2 ? u + a u + b | ? u | 2 + u 3 = g ( x , t ) . It is shown that a pullback attractor exists when its external force has exponential growth. Due to the nonlinear terms b|?u|2 b | ? u | 2 and u3 u 3 , the estimates are delicate. We overcome this difficulty by imposing the exponential growth condition on the external forcing term g(x,t) g ( x , t ) .
pullback attractor a modified swifthohenberg equation asymptotic compactness