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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.37 no.4 Antofagasta dic. 2018

http://dx.doi.org/10.4067/S0716-09172018000400749 

Articles

New interpretation of elliptic Boundary value problems via invariant embedding approach and Yosida regularization

Nadra Bouarroudj1 

Lekhmissi Belaib2 

Bekkai Messirdi3 

1 ENP Oran Maurice Audin, Department of Mathematics and informatics, Algeria, e-mail: nadra_belaib@yahoo.fr

2 University of Oran 1 Ahmed Ben Bella, Department of Mathematics, Oran, Algeria, e-mail: belaib_lekhmissi@yahoo.fr

3 Laboratory of Fundamental and Applicable Mathematics of Oran (LMFAO), Algeria, e-mail: bmessirdi@yahoo.fr

Abstract

The method of invariant embedding for the solutions of boundary value problems yields an equivalent formulation to the initial boundary value problems by a system of Riccati operator differential equations. A combined technique based on invariant embedding approach and Yosida regularization is proposed in this paper for solving abstract Riccati problems and Dirichlet problems for the Poisson equation over a circular domain. We exhibit, in polar coordinates, the associated Neumann to Dirichlet operator, somme concrete properties of this operator are given. It also comes that from the existence of a solution for the corresponding Riccati equation, the problem can be solved in appropriate Sobolev spaces.

Keywords: Elliptic boundary value problems; Invariant embedding method; Riccati operator differential equations; Yosida regularization; Neumann to Dirichlet operator

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgement.

Authors are thankful to the honorable referee for valuable suggestions to improve the paper.

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Received: March 2018; Accepted: July 2018

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