RT Journal Article
T1 Study of the Initial Value Problems Appearing in a Factorization Method of Second Order Elliptic Boundary Value Problems
A1 Ramos Del Olmo, Ángel Manuel
A1 Henry, J.
AB 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.
PB Elsevier
SN 0362-546X
YR 2008
FD 2008-05-15
LK https://hdl.handle.net/20.500.14352/49622
UL https://hdl.handle.net/20.500.14352/49622
LA eng
NO Plan Nacional de I+D+I del MCYT
NO Consejería de Educación de la Comunidad de Madrid
NO Universidad Complutense de Madrid
DS Docta Complutense
RD 21 abr 2025