×

Pullback attractor for a dynamic boundary non-autonomous problem with infinite delay. (English) Zbl 1415.35058

Authors’ abstract: In this work we prove the existence of solution for a \(p\)-Laplacian non-autonomous problem with dynamic boundary and infinite delay. We ensure the existence of pullback attractor for the multivalued process associated to the non-autonomous problem we are concerned.

MSC:

35B41 Attractors
37B55 Topological dynamics of nonautonomous systems
35K92 Quasilinear parabolic equations with \(p\)-Laplacian
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2011. · Zbl 1220.46002
[2] T. Caraballo; P. Marín-Rubio; J. Real; J. Valero, Attractors for differential equations with unbounded delays, J. Differential Equations, 239, 311-342 (2007) · Zbl 1135.34040 · doi:10.1016/j.jde.2007.05.015
[3] T. Caraballo; P. Marín-Rubio; J. Real; J. Valero, Autonomous and non-autonomous attractors for differential equations with delays, J. Differential Equations, 208, 9-41 (2005) · Zbl 1074.34070 · doi:10.1016/j.jde.2003.09.008
[4] V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, Amer. Math. Soc., Providence, RI, 2002. · Zbl 0986.35001
[5] J. Escher, Quasilinear parabolic systems with dynamical boundary conditions, Communications in Partial Differential Equations, 18, 1309-1364 (1993) · Zbl 0816.35059 · doi:10.1080/03605309308820976
[6] A. Favini; G. R. Goldstein; J. A. Goldstein; S. Romanelli, The heat equation with generalized Wentzell boundary condition, J. Evol. Equations, 2, 1-19 (2002) · Zbl 1043.35062 · doi:10.1007/s00028-002-8077-y
[7] C. Gal; M. Warma, Well posedness and the global attractor of some quasi-linear parabolic equations with nonlinear dynamic boundary conditions, Diff. and Int. Equations, 23, 327-358 (2010) · Zbl 1240.35307
[8] C. Gal, On a class of degenerate parabolic equations with dynamic boundary conditions, Journal of Differential Equations, 253, 126-166 (2012) · Zbl 1270.35281 · doi:10.1016/j.jde.2012.02.010
[9] J. K. Hale; J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21, 11-41 (1978) · Zbl 0383.34055
[10] Y. Hino, S. Murakami and T. Naito, Functional Differential Equations with Infinite Delay, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1991. · Zbl 0732.34051
[11] T. Hintermann, Evolution equations with dynamic boundary conditions, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 113, 43-60 (1989) · Zbl 0699.35045 · doi:10.1017/S0308210500023945
[12] F. Li; B. You, Pullback attractors for non-autonomous p-laplacian equations with dynamic flux boundary conditions, Elet. J. of Diff. Equations, 2014, 1-11 (2014) · Zbl 1288.35107
[13] J. L. Lions and E. Megenes, Non-Homogeneous Boundary Value Problems and Applications Vol. Ⅰ, Springer-Verlag Berlin Heidelberg New York, 1972.
[14] A. Z. Manitius, Feedback controllers for a wind tunnel model involving a delay: Analytical design and numerical simulation, IEEE Trans. Automat. Control, 29, 1058-1068 (1984) · doi:10.1109/TAC.1984.1103436
[15] P. Marín-Rubio; A. M. Márquez-Durán; J. Real, Pullback attractors for globally modified Navier-Stokes equations with infinite delays, Disc. and Continuous Dynamical Systems Series A, 31, 779-796 (2011) · Zbl 1250.35042 · doi:10.3934/dcds.2011.31.779
[16] P. Marín-Rubio; A. M. Márquez-Durán; J. Real, Three dimensional system of globally modified Navier-Stokes equations with infinite delays, Discrete and cont. dynamical systems. Series B, 14, 655-673 (2010) · Zbl 1200.35218 · doi:10.3934/dcdsb.2010.14.655
[17] P. Marín-Rubio; J. Real; J. Valero, Pullback attractors for two-dimensional Navier-Stokes model in an infinite delay case, Nonlinear Analysis, 74, 2012-2030 (2011) · Zbl 1218.35045 · doi:10.1016/j.na.2010.11.008
[18] R. A. Samprogna, K. Schiabel and C. B. Gentile Moussa, Pullback attractors for multivalued process and application to nonautonomous problem with dynamic boundary conditions, Set-Valued and Variational Analysis, accepted, 2017.
[19] Y. Wang; P. E. Kloeden, Pullback attractors of a multi-valued process generated by parabolic differential equations with unbounded delays, Nonlinear Analysis, 90, 86-95 (2013) · Zbl 1282.35398 · doi:10.1016/j.na.2013.05.026
[20] L. Yang; M. Yang; P. E. Kloeden, Pullback attractors for non-autonomous quasilinear parabolic equations with dynamical boundary conditions, Disc. and Cont. Dynamical Systems B, 17, 1-11 (2012) · Zbl 1261.37033 · doi:10.3934/dcdsb.2012.17.2635
[21] L. Yang; M. Yang; J. Wu, On uniform attractors for non-autonomous p-Laplacian equation with a dynamic boundary condition, Topological Methods in Nonlinear Analysis, 42, 169-180 (2013) · Zbl 1343.35144
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.