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

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...

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Autores principales:	Bouarroudj,Nadra, Belaib,Lekhmissi, Messirdi,Bekkai
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2018
Materias:	Elliptic boundary value problems Invariant embedding method Riccati operator differential equations Yosida regularization Neumann to Dirichlet operator
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000400749
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spelling	oai:scielo:S0716-091720180004007492018-11-05New interpretation of elliptic Boundary value problems via invariant embedding approach and Yosida regularizationBouarroudj,NadraBelaib,LekhmissiMessirdi,Bekkai Elliptic boundary value problems Invariant embedding method Riccati operator differential equations Yosida regularization Neumann to Dirichlet operator 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.37 n.4 20182018-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000400749en10.4067/S0716-09172018000400749
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Elliptic boundary value problems Invariant embedding method Riccati operator differential equations Yosida regularization Neumann to Dirichlet operator
spellingShingle	Elliptic boundary value problems Invariant embedding method Riccati operator differential equations Yosida regularization Neumann to Dirichlet operator Bouarroudj,Nadra Belaib,Lekhmissi Messirdi,Bekkai New interpretation of elliptic Boundary value problems via invariant embedding approach and Yosida regularization
description	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.
author	Bouarroudj,Nadra Belaib,Lekhmissi Messirdi,Bekkai
author_facet	Bouarroudj,Nadra Belaib,Lekhmissi Messirdi,Bekkai
author_sort	Bouarroudj,Nadra
title	New interpretation of elliptic Boundary value problems via invariant embedding approach and Yosida regularization
title_short	New interpretation of elliptic Boundary value problems via invariant embedding approach and Yosida regularization
title_full	New interpretation of elliptic Boundary value problems via invariant embedding approach and Yosida regularization
title_fullStr	New interpretation of elliptic Boundary value problems via invariant embedding approach and Yosida regularization
title_full_unstemmed	New interpretation of elliptic Boundary value problems via invariant embedding approach and Yosida regularization
title_sort	new interpretation of elliptic boundary value problems via invariant embedding approach and yosida regularization
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2018
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000400749
work_keys_str_mv	AT bouarroudjnadra newinterpretationofellipticboundaryvalueproblemsviainvariantembeddingapproachandyosidaregularization AT belaiblekhmissi newinterpretationofellipticboundaryvalueproblemsviainvariantembeddingapproachandyosidaregularization AT messirdibekkai newinterpretationofellipticboundaryvalueproblemsviainvariantembeddingapproachandyosidaregularization
_version_	1718439841463533568

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

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