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. 2984-3008. ISSN 0362-546X
Official URL: http://www.sciencedirect.com/science/journal/0362546X
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.
|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|
|Deposited On:||15 Mar 2011 14:23|
|Last Modified:||15 Mar 2011 14:23|
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