Controllability for some integrodifferential equations driven by vector measures. (9th August 2016)

• Record Type: Journal Article
• Authors: Dieye, Moustapha; Diop, Mamadou Abdoul; Ezzinbi, Khalil
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 6(2017)
• Page Start: 2090
• Page End: 2106
• Publication Date: 2016-08-09
• Subjects: integrodifferential equations -- controlability -- vector‐valued measures -- resolvent operators -- Pettis' measurability -- Hilbert spaces; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4125
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this work, we consider the question of controllability of a class of integrodifferential equations on Hilbert space with measures as controls. We assume that the linear part has a resolvent operator in the sense given by R. Grimmer. We generalize the original work of N. Ahmed on vector measures, and we use it to develop necessary and sufficient conditions for weak and the exact controllability of the integrodifferential equation. Using the latter, we prove that exact controllability of the integrodifferential equation implies exact controllability of a perturbed integrodifferential equation. Controllability problem for the perturbed system is formulated fixed point problem in the space of vector measures. Our results cover impulsive controls as well as regular controls. Copyright © 2016 John Wiley & Sons, Ltd.