Universidad Complutense de Madrid
E-Prints Complutense

Study of the Initial Value Problems Appearing in a Factorization Method of Second Order Elliptic Boundary Value Problems

Impacto

Downloads

Downloads per month over past year



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

[img]
Preview
PDF
338kB

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
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

Origin of downloads

Repository Staff Only: item control page