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Exact controllability to the trajectories for parabolic PDEs with nonlocal nonlinearities
This paper deals with the analysis of the internal control of a parabolic PDE with nonlinear diffusion, nonlocal in space. In our main result, we prove the local exact controllability to the trajectories with distributed controls, locally supported in space. The main ingredients of the proof are a c...
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Published in: | Mathematics of control, signals, and systems signals, and systems, 2019-09, Vol.31 (3), p.415-431 |
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creator | Fernández-Cara, Enrique Límaco, J. Nina-Huaman, Dany Núñez-Chávez, Miguel R. |
description | This paper deals with the analysis of the internal control of a parabolic PDE with nonlinear diffusion, nonlocal in space. In our main result, we prove the local exact controllability to the trajectories with distributed controls, locally supported in space. The main ingredients of the proof are a compactness–uniqueness argument and Kakutani’s fixed-point theorem in a suitable functional setting. Some possible extensions and open problems concerning other nonlocal systems are presented. |
doi_str_mv | 10.1007/s00498-019-00244-9 |
format | article |
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subjects | Communications Engineering Control Controllability Fixed points (mathematics) Mathematics Mathematics and Statistics Mechatronics Networks Original Article Parabolic differential equations Robotics Stability Systems Theory Trajectory control |
title | Exact controllability to the trajectories for parabolic PDEs with nonlocal nonlinearities |
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