Geodesic
Theoretical analysis and control results for the Fitzhugh-Nagumo equation
Electronic Journal of Differential Equations, Tome 2008 (2008).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we are concerned with some theoretical questions for the FitzHugh-Nagumo equation. First, we recall the system, we briefly explain the meaning of the variables and we present a simple proof of the existence and uniqueness of strong solution. We also consider an optimal control problem for this system. In this context, the goal is to determine how can we act on the system in order to get good properties. We prove the existence of optimal state-control pairs and, as an application of the Dubovitski-Milyoutin formalism, we deduce the corresponding optimality system. We also connect the optimal control problem with a controllability question and we construct a sequence of controls that produce solutions that converge strongly to desired states. This provides a strategy to make the system behave as desired. Finally, we present some open questions related to the control of this equation.
Classification : 35B37, 49J20, 93B05
Keywords: optimal control, controllability, Fitzhugh-Nagumo equation, dubovitski-milyoutin 
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     author = {Brandao, Adilson J.V. and Fernandez-Cara, Enrique and Magalhaes, Paulo M.D. and Rojas-Medar, Marko Antonio},
     title = {Theoretical analysis and control results for the {Fitzhugh-Nagumo} equation},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2008},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a80/}
}
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Brandao, Adilson J.V.; Fernandez-Cara, Enrique; Magalhaes, Paulo M.D.; Rojas-Medar, Marko Antonio. Theoretical analysis and control results for the Fitzhugh-Nagumo equation. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a80/