Existence of Compact Global Attractors for Autonomous Evolution Inclusions

Pengxian ZHU

Abstract


This paper is concentrate with the existence of a compact global attractor for the m-semiflow generated by the autonomous evolution inclusion. Since the lack of compactness of the evolution family, the main tool used in the paper is measure of noncompactness (MNC).


Keywords


Evolution inclusion; Global attractor; m-semiflow; Measures of noncompactness

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References


Andres, J., & Pavlackova, M. (2010). Topological structure of solution sets to asymptotic boundary value problems. J. Differential Equations, 248, 127-150.

Chen, D. H., & Wang, R. N., Zhou, Y. (2013). Nonlinear evolution inclusions: Topological characterizations of solution sets and applications. J. Functional Analysis, 265, 2039-2073.

Chepyzhov, V. V., & Vishik, M. I. (2002). Attractors for equations of mathematics physics. American Mathematical Society Colloquium Publications, 49.

Donchev, T., & Farkhi, E., & Mordukhovich, B. S. (2007). Discrete approximations, relaxation, and optimization of one-sided Lipschitzian differential inclusions in Hilbert spaces. J. Differential Equations, 243, 301-328.

Gabor, G. (2002). On existence of solutions to differential equations or inclusions remaining in a prescribed closed subset of a finite-dimensional space. J. Differential Equations, 185, 483-512.

Gabor, G., & Grudzka, A. (2012). Structure of the solution set to impulsive functional differential inclusions on the half-line. Nonlinear Differ. Equ. Appl., 19, 609-627.

Halanay, (1966). A. differential equations, stability, oscillations, time lags. New York, London: Academic Press.

Kamenskii, M., & Obukhovskii, V., & Zecca, P. (2001). Condensing multi-valued maps and semilinear differential inclusions in banach spaces. de Gruyter Series in Nonlinear Analysis and Applications, 7.

Melnik, V.S., & Valero, J. (1998). On attractors of multivalued semi-flows and differential inclusions. Set-Valued Anal., 6, 83-111.

O’Regan, D., & Precup, R. (2001). Existence criteria for integral equations in Banach spaces. J. Inequal. Appl., 6, 77-97.

Temam, R. (1997). Infinite dimensional dynamical systems in mechanics and physics (2nd ed.). Springer-Verlag.

Wang, W. (2010). A generalized Halanay inequality for stability of nonlinear neutral functional differential equations. J. Inequal. Appl. Art., ID 475019.




DOI: http://dx.doi.org/10.3968/9699

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