On a Direct Study of an Operator Riccati Equation Appearing in Boundary Value Problems Factorization

Nadra Bouarroudj , Jacques Henry (1, 2) , Bento Louro , Maria Orey

1 IMB - Institut de Mathématiques de Bordeaux
2 ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics

In this paper we propose a direct study of the Riccati equation satisfied by the Dirichlet-Neumann operator defined on a moving section for an elliptic boundary value problem set in a cylindrical domain [3]. Similar equations are studied in control theory. The additional difficulty of this problem is due to the unboundedness of the right-hand side and of the solution of the equation. The Yosida regularization is used to overcome it.

Mots clés: Factorization; boundary value problem; operator Riccati equation; Dirichlet to Neumann operator; Yosida regularization

Domaines: Equations aux dérivées partielles [math.AP]

Nadra Bouarroudj, Jacques Henry, Bento Louro, Maria Orey. On a Direct Study of an Operator Riccati Equation Appearing in Boundary Value Problems Factorization. Applied Mathematical Sciences, 2008, 2 (46), pp.2247 - 2257. ⟨inria-00387563⟩