an:01783099
Zbl 1001.37012
Cheban, D. N.; Schmalfuss, B.
Global attractors of nonautonomous disperse dynamical systems and differential inclusions
EN
Bul. Acad. ??tiin??e Repub. Mold., Mat. 1999, No. 1(29), 3-22 (1999).
00057752
1999
j
37B55 34A60 34D45 34K06 37B25
nonautonomous dynamical systems; multivalued maps; attractors
The authors study the longtime behavior of abstract nonautonomous dynamical systems without uniqueness. The main result of the paper is the extention of the attractors theory to the class of dissipative nonautonomous dynamical systems generated by multivalued (set-valued) operators. The applications of the obtained results to ordinary differential equations with non Lipschitz nonlinearities, differential inclusions and functional-differential equations are also considered. The alternative approach to nonautonomous dynamical systems without uniqueness which is based on the concept of a trajectory dynamical system and trajectory attractors can be found in [\textit{V. V. Chepyzhov} and \textit{M. I. Vishik}, Attractors for equations of mathematical physics. Colloquium Publications. 49. Providence, RI: American Mathematical Society (2002; Zbl 0986.35001)].
Serguei Zelik (Chasseneuil Futuroscope)
Zbl 0986.35001