Abstract
In this paper we describe and develop a method first proposed by Angel and Bellman ([1]) to factorize a second order elliptic boundary value problem in the product of two first order decoupled initial value problems by invariant embeding. For the sake of simplicity we consider a domain Ω of ℝ n which is a cylinder ]0, 1[× O and the Laplacian Δ as elliptic operator. We denote x the coordinate along the first axis which is also the axis of the cylinder and y the n − 1 other coordinates. The section O ⊂ ℝ n−1 is bounded and has a smooth boundary. We denote Σ =]0,1[×∂O the lateral boundary of the cylinder and Γ0 = {0} × 0, Γ1 = {1} × O the two faces of the cylinder.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35690-7_44
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Angel E., Bellman R. Dynamic Programming and Partial Differential Equations Academic Press 1972.
Henry J., Ramos A. Factorization of Second Order Elliptic Boundary Value Problems by Dynamic Programming,submitted to Journal Math. Ana. Appl.
Henry, J., Ramos, A. A Direct Study in a Hilbert-Schmidt Framework of the Riccati Equation Appearing in a Factorization Method of Second Order Elliptic Boundary Value Problems Rapport de Recherche INRIA 4451.
Lions, J.L. (1968). Contrôle Optimal de Systèmes Gouvernés par des Équations aux Dérivées Partielles. Dunod.
Lions, J.L., and Magenes E. (1968). Problèmes aux Limites Non Homogènes et Applications,vol 1. Dunod.
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© 2003 IFIP International Federation for Information Processing
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Henry, J. (2003). Factorization of Elliptic Boundary Value Problems: The QR Approach. In: Barbu, V., Lasiecka, I., Tiba, D., Varsan, C. (eds) Analysis and Optimization of Differential Systems. SEC 2002. IFIP — The International Federation for Information Processing, vol 121. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35690-7_20
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DOI: https://doi.org/10.1007/978-0-387-35690-7_20
Publisher Name: Springer, Boston, MA
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