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Ramos del Olmo, Ángel Manuel and Henry, J.
(2008)
*Study of the Initial Value Problems Appearing in a Factorization Method of Second Order Elliptic Boundary Value Problems.*
Nonlinear Analysis: Theory, Methods & Applications, 68
(10).
pp. 2984-3008.
ISSN 0362-546X

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Official URL: http://www.sciencedirect.com/science/journal/0362546X

## Abstract

In [J. Henry, A.M. Ramos, Factorization of second order elliptic boundary value problems by dynamic programming, Nonlinear Analysis. Theory, Methods & Applications 59 (2004) 629–647] we presented a method for factorizing a second-order boundary value problem into a system of uncoupled first-order initial value problems, together with a nonlinear Riccati type equation for functional operators. A weak sense was given to that system but we did not perform a direct study of those equations. This factorization utilizes either the Neumann to Dirichlet (NtD) operator or the Dirichlet to Neumann (DtN) operator, which satisfy a Riccati equation. Here we consider the framework of Hilbert–Schmidt operators, which provides tools for a direct study of this Riccati type equation. Once we have solved the system of Cauchy problems, we show that its solution solves the original second-order boundary value problem. Finally, we indicate how this techniques can be used to find suitable transparent conditions.

Item Type: | Article |
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Uncontrolled Keywords: | Factorization; Boundary value problem; Hilbert–Schmidt operator; Riccati equation; Invariant embedding; Neumann to Dirichlet (NtD) operator; Dirichlet to Neumann (DtN) operator; Transparent conditions |

Subjects: | Sciences > Mathematics > Mathematical analysis |

ID Code: | 12426 |

Deposited On: | 15 Mar 2011 13:23 |

Last Modified: | 12 Dec 2018 15:07 |

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