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2004 | 24 | 1 | 49-72
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Controllability of evolution equations and inclusions driven by vector measures

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In this paper, we consider the question of controllability of a class of linear and semilinear evolution equations on Hilbert space with measures as controls. We present necessary and sufficient conditions for weak and exact (strong) controllability of a linear system. Using this result we prove that exact controllability of the linear system implies exact controllability of a perturbed semilinear system. Controllability problem for the semilinear system is formulated as a fixed point problem on the space of vector measures and is concluded controllability from the existence of a fixed point. Our results cover impulsive controls as well as regular controls.
  • School of Information Technology and Engineering and Department of Mathematics, University of Ottawa, Ottawa, Ontario K1N6N5
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