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A Direct Study in a Hilbert-Schmidt Framework of the Riccati Equation Appearing in a Factorization Method of Second Order Elliptic Boundary Value Problems

Jacques Henry 1 Angel M. Ramos 1
1 ONDES - Modeling, analysis and simulation of wave propagation phenomena
Inria Paris-Rocquencourt, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR2706
Abstract : In this report we come back to the method of factorization of a second order elliptic boundary value problem presented in . In this paper, it was shown that, in the case of a cylinder, the boundary value problem can be factorized in two uncoupled first order initial value problems. This factorization utilizes the Dirichlet to Neumann operator which satisfies a Riccati equation. Here we consider Hilbert-Schmidt operators, a framework already used by R. Temam which provides tools for a direct study of this Riccati equation.
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https://hal.inria.fr/inria-00072137
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Submitted on : Tuesday, May 23, 2006 - 7:53:13 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:04 PM
Long-term archiving on: : Sunday, April 4, 2010 - 10:54:59 PM

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Jacques Henry, Angel M. Ramos. A Direct Study in a Hilbert-Schmidt Framework of the Riccati Equation Appearing in a Factorization Method of Second Order Elliptic Boundary Value Problems. [Research Report] RR-4451, INRIA. 2002. ⟨inria-00072137⟩

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