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Mathematical Problems in Engineering
Volume 2016, Article ID 2468458, 6 pages
http://dx.doi.org/10.1155/2016/2468458
Research Article

Stability and Boundedness of Solutions to Nonautonomous Parabolic Integrodifferential Equations

Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel

Received 20 January 2016; Revised 24 April 2016; Accepted 3 May 2016

Academic Editor: Quanxin Zhu

Copyright © 2016 Michael Gil'. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a class of linear nonautonomous parabolic integrodifferential equations. We will assume that the coefficients are slowly varying in time. Conditions for the boundedness and stability of solutions to the considered equations are suggested. Our results are based on a combined usage of the recent norm estimates for operator functions and theory of equations on the tensor product of Hilbert spaces.