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Pullback exponential attractors for nonautonomous dynamical system in space of higher regularity |
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| Authors: | Yongjun Li Tinggang Zhao Hongqing Wu and Jinying Wei |
| Institution: | School of Mathematics,Lanzhou City University,No.11,Jiefang Road, 730070, China,School of Mathematics,Lanzhou City University,No.11,Jiefang Road, 730070, China,School of Mathematics,Lanzhou City University,No.11,Jiefang Road, 730070, China and School of Mathematics,Lanzhou City University,No.11,Jiefang Road, 730070, China |
| Abstract: | Under what condition, a process which exists a $(E,E)$-pullback exponential attractor implies the existence of $(E,V)$- pullback exponential attractor when $V$ embedded in $E$? We answer this question in this paper. As an application of this result, we prove the existence of pullback exponential attractor for a nonlinear reaction-diffusion equation with a polynomial growth nonlinearity in $L^q(\Omega)(\forall q\geq 2)$ and $H_0^1(\Omega)$. |
| Keywords: | Nonautonomous dynamical system fractal dimension pullback exponential attractors reaction diffusion equation |
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