Attractors for families of processes in weak topologies of banach spaces

Discrete and Continuous Dynamical Systems

Volumn 4, Issue 3, 1998, Pages 455-466

  Gazzola, Filippo ^a   Sardella, Mirko ^b  

^a UNIVERSITY OF EASTERN PIEDMONT   (Italy)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

Compactification at infinity; Processes

Indexed keywords

EID: 0032366877     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.1998.4.455     Document Type: Article

References (25)

1. A. Arosio, A simple presentation of attractors for abstract dynamical systems, in preparation
2. A.V. Babin and M.I. Vishik, "Attractors of Evolution Equations," North-Holland, Amsterdam, 1992.
3. J.M. Ball, Stability theory for an extensible beam, J. Diff. Eqns., 14 (1973), 399-418.
4. J.M. Ball, On the asymptotic behavior of generalized processes, with applications to nonlinear evolution equations, J. Diff. Eqns., 27 (1978), 224-265.
5. J.M. Ball and M. Slemrod, Feedback stabilization of distributed semilinear control systems, Appl. Math. Optim., 5 (1979), 169-179.
6. V.V. Chepyzhov and M.I. Vishik, Nonautonomous evolution equations and their attractors, Russian J. Math. Phys., 1 (1993), 165-190.
7. V.V. Chepyzhov and M.I. Vishik, Attractors of non-autonomous dynamical systems and their dimension, J. Math. Pures Appl., 73 (1994), 279-333.
8. V. V. Chepyzhov and M.I. Vishik, Non-autonomous evolutionary equations with translation compact symbols and their attractors, C. R. Acad. Sci. Paris Sér. I Math., 321 (1995), 153-158.
9. C.M. Dafermos, An invariance principle for compact processes, J. Diff. Eqns., 9 (1971), 235-252.
10. C.M. Dafermos, Applications of the invariance principle for compact processes. I. Asymptotically dynamical systems, J. Diff. Eqns., 9 (1971), 291-299.
11. F. Gazzola, An attractor for a 3D Navier-Stokes type equation, Zeit. Anal. Anwend., 14 (1995), 509-522.
12. F. Gazzola and V. Pata, A uniform attractor for a nonautonomous generalized Navier-Stokes equation, Zeit. Anal. Anwend., 16 (1997), 435-449.
13. J.M. Ghidaglia, Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical system in the long time, J. Diff. Eqns., 74 (1988), 369-390.
14. J.M. Ghidaglia, A note on the strong convergence towards attractors of damped forced KdV equations, J. Diff. Eqns., 110 (1994), 356-359.
15. M. Gobbino and M. Sardella, On the connectedness of attractors for dynamical systems, J. Diff. Eqns., 133 (1997), 1-14.
16. J.K. Hale, "Asymptotic Behavior of Dissipative Systems," Math. Surv. Monog., vol. 25, AMS, 1988.
17. J.K. Hale and N. Stavrakakis, Compact attractors for weak dynamical systems, Appl. Anal., 26 (1988), 271-287.
18. A. Haraux, "Systèmes Dynamiques Dissipatifs et Applications," Masson, Paris, 1991.
19. Jin Liang and Qin Tiehu, Asymptotic behaviour of weak solutions to a boundary value problem for dynamic viscoelastic equations with memory, Proc. Roy. Soc. Edinburgh, 125 (A) (1995), 153-164.
20. O.A. Ladyzhenskaya, Attractors for fully nonlinear parabolic equations of second order, Rend. Mat. Serie VII, 10 (1990), 749-756.
21. O.A. Ladyzhenskaya, "Attractors for Semigroups and Evolution Equations," Lezioni Lincee, Acc. Naz. Lincei, Cambridge University Press, 1991.
22. G. Prouse, On a Navier-Stokes type equation in "Nonlinear Analysis: a tribute in honour of Giovanni Prodi," (Ed. A. Ambrosetti and A. Marino), Quaderni Sc. Norm. Sup. Pisa, 1991, 289-305.
23. G.R. Sell, Nonautonomous differential equations and topological dynamics I, II, Trans. Amer. Math. Soc., 127 (1967), 241-262; 263-283.
24. M. Slemrod, Asymptotic behavior of a class of abstract dynamical systems, J. Diff. Eqns., 7 (1970), 584-600.
25. R. Temam, "Infinite Dimensional Dynamical Systems in Mechanics and Physics," Springer-Verlag, New York, 1988.