Coayla-Teran EA, Ferreira J, de Magalhães PMD.
Weak solutions for random nonlinear parabolic equations of nonlocal type. Random Operators/Stochastic Equations. 2008;16:213-222.
AbstractThe existence and uniqueness of weak solutions for a random version of a class ofnonlinear parabolic problems of nonlocal type with additive noise are studied.
Adilson J.V. Brandão, Enrique Fernández-Cara PMDMMAR-M.
Theoretical analysis and control results for the FitzHugh-Nagumo equation. Eletronic Journal of Differential Equations. 2008;2008(164):1-20.
AbstractIn this paper we are concerned with some theoretical questions forthe 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.