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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Bibliographic Details
Published in:Mathematics of control, signals, and systems signals, and systems, 2019-09, Vol.31 (3), p.415-431
Main Authors: Fernández-Cara, Enrique, Límaco, J., Nina-Huaman, Dany, Núñez-Chávez, Miguel R.
Format: Article
Language:English
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
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Summary: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.
ISSN:0932-4194
1435-568X
DOI:10.1007/s00498-019-00244-9