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Universidade Federal Fluminense
J. Límaco, Miguel R. Nuñez-Chávez, and Dany Nina Huaman
Nonlinear Analysis, Theory, Methods and Applications, ISSN: 0362546X, Volume: 214, Published: January 2022 Elsevier BV
Dany Nina-Huaman and J. Límaco
Applied Mathematics and Optimization, ISSN: 00954616, eISSN: 14320606, Published: 2021 Springer Science and Business Media LLC
Dany Nina Huaman
Journal of Dynamical and Control Systems, ISSN: 10792724, eISSN: 15738698, Published: 2021 Springer Science and Business Media LLC
This paper deals with the application of Stackelberg-Nash strategies to the control to quasi-linear parabolic equations in dimensions 1D, 2D, or 3D. We consider two followers, intended to solve a Nash multi-objective equilibrium; and one leader satisfying the controllability to the trajectories.
Enrique Fernández-Cara, J. Límaco, Dany Nina-Huaman, and Miguel R. Núñez-Chávez
Mathematics of Control, Signals, and Systems, ISSN: 09324194, eISSN: 1435568X, Pages: 415-431, Published: 1 September 2019 Springer Science and Business Media LLC
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.
Dany Nina Huaman, Juan Límaco, and Miguel R. Nuñez Chávez
SEMA SIMAI Springer Series, ISSN: 21993041, eISSN: 2199305X, Pages: 139-158, Published: 2018 Springer International Publishing
This paper deals with the null controllability of a differential turbulence model of the Ladyzhenskaya-Smagorinsky kind. In the equations, we find local and nonlocal nonlinearities: the usual transport terms and a turbulent viscosity that depends on the global in space energy dissipated by the mean flow. We prove that the N-systems are locally null-controllable with N-1 scalar controls in an arbitrary control domain.
Enrique Fernández-Cara, Dany Nina-Huamán, Miguel R. Nuñez-Chávez, and Franciane B. Vieira
Journal of Optimization Theory and Applications, ISSN: 00223239, eISSN: 15732878, Volume: 175, Pages: 652-682, Published: 1 December 2017 Springer Science and Business Media LLC
This paper deals with the analysis of the internal and boundary control of a one-dimensional parabolic partial differential equation with nonlinear diffusion. First, we prove a local null controllability result with distributed controls, locally supported in space. The proof relies on local inversion (more precisely, we use Liusternik’s Inverse Function Theorem), together with some appropriate specific estimates. We also establish a similar result with controls on one side of the boundary. Then, we consider an iterative algorithm for the computation of null controls, we prove the convergence of the iterates, and we perform some numerical experiments.