`a`
Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Pullback attractor for a dynamic boundary non-autonomous problem with infinite delay
Page number are going to be assigned later 2017

doi:10.3934/dcdsb.2017195      Abstract        References        Full text (362.2K)      

Rodrigo Samprogna - Departamento de Matemática, Centro de Ciências Exatas e de Tecnologia, Universidade Federal de São Carlos, Caixa Postal 676, 13.565-905 São Carlos SP, Brazil (email)
Tomás Caraballo - Departamento de Ecuaciones Diferenciales y Análisis Numérico , Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain (email)

1 H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2011.       
2 T. Caraballo, P. Marín-Rubio, J. Real and J. Valero, Attractors for differential equations with unbounded delays, J. Differential Equations, 239 (2007), 311-342.       
3 T. Caraballo, P. Marín-Rubio, J. Real and J. Valero, Autonomous and non-autonomous attractors for differential equations with delays, J. Differential Equations, 208 (2005), 9-41.       
4 V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, Amer. Math. Soc., Providence, RI, 2002.       
5 J. Escher, Quasilinear parabolic systems with dynamical boundary conditions, Communications in partial differential equations, 18 (1993), 1309-1364.       
6 A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, The heat equation with generalized Wentzell boundary condition, J. Evol. Equations, 2 (2002), 1-19.       
7 C. Gal and M. Warma, Well posedness and the global attractor of some quasi-linear parabolic equations with nonlinear dynamic boundary conditions, Diff. and Int. Equations, 23 (2010), 327-358.       
8 C. Gal, On a class of degenerate parabolic equations with dynamic boundary conditions, Journal of Differential Equations, 253 (2012), 126-166.       
9 J. K. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21 (1978), 11-41.       
10 Y. Hino, S. Murakami and T. Naito, Functional Differential Equations with Infinite Delay, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1991.       
11 T. Hintermann, Evolution equations with dynamic boundary conditions, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 113 (1989), 43-60.       
12 F. Li and B. You, Pullback attractors for non-autonomous p-laplacian equations with dynamic flux boundary conditions, Elet. J. of Diff. Equations, 2014 (2014), 1-11.       
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 (1984), 1058-1068.       
15 P. Marín-Rubio, A. M. Márquez-Durán and J. Real, Pullback attractors for globally modified Navier-Stokes equations with infinite delays, Disc. and Continuous Dynamical Systems Series A, 31 (2011), 779-796.       
16 P. Marín-Rubio, A. M. Márquez-Durán and J. Real, Three dimensional system of globally modified Navier-Stokes equations with infinite delays, Discrete and cont. dynamical systems. Series B, 14 (2010), 655-673.       
17 P. Marín-Rubio, J. Real and J. Valero, Pullback attractors for two-dimensional Navier-Stokes model in an infinite delay case, Nonlinear Analysis, 74 (2011), 2012-2030.       
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 and P. E. Kloeden, Pullback attractors of a multi-valued process generated by parabolic differential equations with unbounded delays, Nonlinear Analysis, 90 (2013), 86-95.       
20 L. Yang, M. Yang and P. E. Kloeden, Pullback attractors for non-autonomous quasilinear parabolic equations with dynamical boundary conditions, Disc. and Cont. Dynamical Systems B, 17 (2012), 1-11.       
21 L. Yang, M. Yang and J. Wu, On uniform attractors for non-autonomous p-Laplacian equation with a dynamic boundary condition, Topological Methods in Nonlinear Analysis, 42 (2013), 169-180.       

Go to top