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Approximate controllability by birth control for a nonlinear population dynamics model

Otared KavianOumar Traoré — 2011

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we analyse an approximate controllability result for a nonlinear population dynamics model. In this model the birth term is nonlocal and describes the recruitment process in newborn individuals population, and the control acts on a small open set of the domain and corresponds to an elimination or a supply of newborn individuals. In our proof we use a unique continuation property for the solution of the heat equation and the Kakutani-Fan-Glicksberg fixed point theorem.

Approximate controllability by birth control for a nonlinear population dynamics model

Otared KavianOumar Traoré — 2011

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we analyse an approximate controllability result for a nonlinear population dynamics model. In this model the birth term is nonlocal and describes the recruitment process in newborn individuals population, and the control acts on a small open set of the domain and corresponds to an elimination or a supply of newborn individuals. In our proof we use a unique continuation property for the solution of the heat equation and the Kakutani-Fan-Glicksberg fixed point theorem.

Determining two coefficients in elliptic operators via boundary spectral data: a uniqueness result

Bruno CanutoOtared Kavian — 2004

Bollettino dell'Unione Matematica Italiana

For a bounded and sufficiently smooth domain Ω in R N , N 2 , let λ k k = 1 and φ k k = 1 be respectively the eigenvalues and the corresponding eigenfunctions of the problem (with Neumann boundary conditions) - div a x φ k + q x φ k = λ k ϱ x φ k  in  Ω , a n φ k = 0  su  Ω . We prove that knowledge of the Dirichlet boundary spectral data λ k k = 1 , φ k | Ω k = 1 determines uniquely the Neumann-to-Dirichlet (or the Steklov- Poincaré) map γ for a related elliptic problem. Under suitable hypothesis on the coefficients a , q , ϱ their identifiability is then proved. We prove also analogous results for Dirichlet...

Unique continuation principle for systems of parabolic equations

Otared KavianLuz de Teresa — 2010

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we prove a unique continuation result for a cascade system of parabolic equations, in which the solution of the first equation is (partially) used as a forcing term for the second equation. As a consequence we prove the existence of -insensitizing controls for some parabolic equations when the control region and the observability region do not intersect.

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