Hamidou Touré

On the stock estimation for some fishery systems

In this work we address the stock estimation problem for two fishery models. We show that a tool from nonlinear control theory called “observer” can be helpful to deal with the resource stock estimation in the field of renewable resource management. It is often difficult or expensive to measure all the state variables characterising the evolution of a given population system, therefore the question arises whether from the observation of certain indicators of the considered system, the whole state of the population system can be recovered or at least estimated. The goal of this paper is to show how some techniques of control theory can be applied for the approximate estimation of the unmeasurable state variables using only the observed data together with the dynamical model describing the evolution of the system. More precisely we shall consider two fishery models and we shall show how to built for each model an auxiliary dynamical system (the observer) that uses the available data (the total of caught fish) and which produces a dynamical estimation

A non Linear Observer for a fishery model

\hat x(t)

Existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces

of the unmeasurable stock state x(t). Moreover the convergence speed of

Local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces

\hat x(t)

An existence result for impulsive functional differential equations with variable times

towards x(t) can be chosen.

Pseudo almost periodic solutions of class r for neutral partial functional differential equations

Resume Nous etudions dans cet article l’equation generale ut = a(., u, φ(., u)x)x + v de type parabolique pouvant degenerer en hyperbolique du premier ordre pour certaines valeurs de (x, u). Utilisant la theorie des semi-groupes non lineaires dans L1, nous etablissons des resultats d’existence, d’unicite et de dependance continue par rapport aux donnees, d’une « bonne solution » du probleme de Cauchy ou de problemes aux limites associes a cette equation sous des hypotheses tres generales sur les donnees. Avec des hypotheses complementaires, nous montrons que cette « bonne solution » est « solution entropique », nous etudions l’unicite des solutions faibles et l’existence de solution forte.