Ramos del Olmo, Ángel 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. 29843008. ISSN 0362546X

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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 secondorder boundary value problem into a system of uncoupled firstorder 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 secondorder boundary value problem. Finally, we indicate how this techniques can be used to find suitable transparent conditions.
Item Type:  Article 

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:  06 Feb 2014 09:24 
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