IJPAM: Volume 74, No. 2 (2012)

ATTRACTORS, APPROXIMATIONS AND
FIXED SETS OF EVOLUTION SYSTEMS

Q. Din$^1$, T. Donchev$^2$, D. Kolev$^3$
$^{1,2}$Abdus Salam School of Mathematical Sciences (ASSMS)
68-B, New Muslim Town, Lahore, PAKISTAN
$^3$Department of Basic Sciences
Academy of Bulgarian Ministry of Internal Affairs (Police Academy)
Sofia, BULGARIA


Abstract. In this paper we study autonomous evolution inclusions in an evolution triple, and satisfying one sided Lipschitzian condition with some negative constant. It is known that the solution set is compact on every bounded interval. Using this fact we prove the existence of a unique strong forward attractor and a unique strong backward attractor when the one sided Lipschitz constant is positive. As a corollary some surjectivity and fixed point results are proved. An example of a parabolic system, satisfying our assumptions is discussed.

Received: August 13, 2011

AMS Subject Classification: 34A60, 34A45, 49J24

Key Words and Phrases: evolution triple, strong attractor, evolution inclusions, one sided Lipschitz, approximations

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 74
Issue: 2