Journal Article10.1016/J.NA.2010.03.023
On pullback attractors in Lp for nonautonomous reaction–diffusion equations☆
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TL;DR: In this paper, the existence of a unique minimal pullback attractor for the evolutionary process associated with a non-autonomous nonlinear reaction diffusion system in L p, p ≥ 2 was proved.
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Abstract: Using the method introduced in Zhong et al. (2006) [17] together with a new way of dealing with well known estimates of solutions introduced in Łukaszewicz (in press) [9] we prove the existence of a unique minimal pullback attractor for the evolutionary process associated with a nonautonomous nonlinear reaction–diffusion system in L p , p ≥ 2 , in which the right hand side satisfies only a certain integrability condition. In particular, we generalize a result obtained recently in Li et al. (2009) [13] where an at most exponential growth of the right hand side has been assumed for times going to both plus and minus infinity.
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Pullback attractors for asymptotically compact non-autonomous dynamical systems
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