Abstract
We consider a nonautonomous inclusion the upper and lower selectors of whose right-hand side are determined by functions with discontinuities of the first kind. We prove that this problem generates a family of multivalued semiprocesses for which there exists a global attractor compact in the phase space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
V. V. Chepyzhov and M. I. Vishik, “Attractors of nonautonomous dynamical systems and their dimension,” J. Math. Pures Appl., 73, No. 3, 279–333 (1994).
V. V. Chepyzhov and M. I. Vishik, “Trajectory attractors for nonautonomous evolution equations,” J. Math. Pures Appl., 76, No. 10, 913–965 (1997).
V. S. Melnik and J. Valero, “On global attractors of multivalued semiprocesses and nonautonomous evolution inclusions,” Set-Valued Analysis, 8, 375–403 (2000).
A. V. Kapustyan, “Global attractors of a nonautonomous reaction-diffusion equation,” Differents. Uravn., 10, 1378–1382 (2002).
I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes [in Russian], Nauka, Moscow (1977).
K. Yosida, Functional Analysis [Russian translation], Mir, Moscow (1967).
J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Berlin (1990).
A. A. Tolstonogov, “On solutions of evolution imbeddings. 1” Sib. Mat. Zh., 33, No. 3, 145–162 (1992).
A. A. Tolstonogov and Ya. I. Umanskii, “On solutions of evolution imbeddings. 2,” Sib. Mat. Zh., 33, No. 4, 163–174 (1992).
V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Acad., Bucuresti (1976).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kapustyan, O.V., Kas'yanov, P.O. Global Attractor for a Nonautonomous Inclusion with Discontinuous Right-Hand Side. Ukrainian Mathematical Journal 55, 1765–1776 (2003). https://doi.org/10.1023/B:UKMA.0000027041.12041.e8
Issue Date:
DOI: https://doi.org/10.1023/B:UKMA.0000027041.12041.e8