Wang, Yonghai; Zhong, Chengkui On the existence of pullback attractors for non-autonomous reaction-diffusion equations. (English) Zbl 1145.35047 Dyn. Syst. 23, No. 1, 1-16 (2008). Summary: We prove the existence of pullback attractors for a nonautonomous nonlinear reaction-diffusion equation with a nonlinearity having a polynomial growth of arbitrary order \(p - 1 (p \geq 2)\). The pullback attractors are obtained in \(H_0^1(\Omega)\). For this purpose, some abstract results are established by the method of measure of noncompactness. Cited in 26 Documents MSC: 35B41 Attractors 35K57 Reaction-diffusion equations 37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations Keywords:polynomially growing nonlinearities; method of measure of noncompactness PDFBibTeX XMLCite \textit{Y. Wang} and \textit{C. Zhong}, Dyn. Syst. 23, No. 1, 1--16 (2008; Zbl 1145.35047) Full Text: DOI References: [1] DOI: 10.1017/S1446181100013274 · Zbl 1047.35024 · doi:10.1017/S1446181100013274 [2] DOI: 10.1142/S0219493704001139 · Zbl 1061.35153 · doi:10.1142/S0219493704001139 [3] DOI: 10.1016/j.na.2005.03.111 · Zbl 1128.37019 · doi:10.1016/j.na.2005.03.111 [4] DOI: 10.1016/j.jde.2004.04.012 · Zbl 1068.35088 · doi:10.1016/j.jde.2004.04.012 [5] Cheban DN, Nonlinear Dynamics and System Theory 2 pp 9– (2002) [6] DOI: 10.1023/A:1009000700546 · Zbl 0999.34054 · doi:10.1023/A:1009000700546 [7] Chepyzhov VV, American Mathematical Society Colloquium 49 (2000) [8] DOI: 10.1007/BF01193705 · Zbl 0819.58023 · doi:10.1007/BF01193705 [9] DOI: 10.1007/BF02219225 · Zbl 0884.58064 · doi:10.1007/BF02219225 [10] Hale JK, Asymptotic Behaviour of Dissipative Systems (1988) [11] DOI: 10.1023/A:1019156812251 · Zbl 0886.65077 · doi:10.1023/A:1019156812251 [12] DOI: 10.1016/S0167-6911(97)00107-2 · Zbl 0902.93043 · doi:10.1016/S0167-6911(97)00107-2 [13] Kloeden PE, Dynamics of Continuous Discrete Impulsive Systems 4 pp 211– (1998) [14] DOI: 10.1007/978-94-010-0732-0 · doi:10.1007/978-94-010-0732-0 [15] DOI: 10.1007/978-1-4757-5037-9 · doi:10.1007/978-1-4757-5037-9 [16] DOI: 10.1016/j.jmaa.2006.02.041 · Zbl 1104.37013 · doi:10.1016/j.jmaa.2006.02.041 [17] DOI: 10.1007/978-1-4612-0645-3 · doi:10.1007/978-1-4612-0645-3 [18] DOI: 10.3934/dcds.2006.16.705 · Zbl 1121.34027 · doi:10.3934/dcds.2006.16.705 [19] DOI: 10.1016/j.jde.2005.06.008 · Zbl 1101.35022 · doi:10.1016/j.jde.2005.06.008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.