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Controllability for some integrodifferential equations driven by vector measures
Author(s) -
Dieye Moustapha,
Diop Mamadou Abdoul,
Ezzinbi Khalil
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4125
Subject(s) - controllability , mathematics , hilbert space , resolvent , work (physics) , class (philosophy) , cover (algebra) , mathematical analysis , space (punctuation) , pure mathematics , computer science , mechanical engineering , artificial intelligence , engineering , operating system
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.