A global attractor for one semilinear hyperbolic equation with memory operator

A. B. Aliyev^ab, S. E. Isayeva<sup>c

a</sup> Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, ul. F. Agaeva 9, Baku, AZ, 1141, Azerbaijan
^b Azerbaijan Technical University, pr. H.Cavid 25, Baku, AZ, 1073, Azerbaijan
^c Baku State University, ul. Akademika Z. Khalilova 23, Baku, AZ, 1148, Azerbaijan

Abstract: The mixed problem for a semilinear hyperbolic equation with a memory operator is considered. The existence of a minimal global attractor for this problem is proved.

Key words: minimal global attractor, hysteresis, memory operator, semilinear hyperbolic equation.

UDC: 519.63

MSC: Primary 5L72; Secondary 35B40, 35B41, 35L20

Received: 07.07.2014

DOI: 10.7868/S0044466915110034

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:11, 1823–1835

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