Theoretical analysis and control results for the Fitzhugh-Nagumo equation

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

Hodge operator and asymmetric fluid in unbounded domains

A system of equations modeling the stationary flow of an incompressible asymmetric fluid is studied for bounded domains of an arbitrary form. Based on the methods of Clifford analysis, we write the system of asymmetric fluid in the hypercomplex formulation and represent its solution in Clifford operator terms. We have significantly used Clifford algebra, and in particular the Hodge operator of the Clifford algebra to demonstrate the existence and uniqueness of the strong solution for arbitrary unbounded domainsA system of equations modeling the stationary flow of an incompressible asymmetric fluid is studied for bounded domains of an arbitrary form. Based on the methods of Clifford analysis, we write the system of asymmetric fluid in the hypercomplex formulation and represent its solution in Clifford operator terms. We have significantly used Clifford algebra, and in particular the Hodge operator of the Clifford algebra to demonstrate the existence and uniqueness of the strong solution for arbitrary unbounded domain

Hodge operator and asymmetric fluid in unbounded domains

A system of equations modeling the stationary flow of an incompressible asymmetric fluid is studied for bounded domains of an arbitrary form. Based on the methods of Clifford analysis, we write the system of asymmetric fluid in the hypercomplex formulation and represent its solution in Clifford operator terms. We have significantly used Clifford algebra, and in particular the Hodge operator of the Clifford algebra to demonstrate the existence and uniqueness of the strong solution for arbitrary unbounded domain

Reproductive solution for grade-two fluid model in two dimensions

  We treat the existence of reproductive solution (weak periodic solution) of a second-grade fluid system in two dimensions, by using the Galerkin approximation method and compactness arguments.   We treat the existence of reproductive solution (weak periodic solution) of a second-grade fluid system in two dimensions, by using the Galerkin approximation method and compactness arguments.&nbsp

Continuity for s-convex fuzzy processes

In a previous paper we introduced the concept of s-convex fuzzy mapping and established some properties. In this work we study the continuity for s-convex fuzzy processes