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

  • Nadra Bouarroudj ENP Oran Maurice Audin.
  • Lekhmissi Belaib University of Oran 1 Ahmed Ben Bella.
  • Bekkai Messirdi Laboratory of Fundamental and Applicable Mathematics of Oran. https://orcid.org/0000-0001-6077-4073

Resumen

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.

Biografía del autor

Nadra Bouarroudj, ENP Oran Maurice Audin.
Department of Mathematics and informatics.
Lekhmissi Belaib, University of Oran 1 Ahmed Ben Bella.
Department of Mathematics.

Citas

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Publicado
2018-11-22
Cómo citar
Bouarroudj, N., Belaib, L., & Messirdi, B. (2018). New interpretation of elliptic Boundary value problems via invariant embedding approach and Yosida regularization. Proyecciones. Revista De Matemática, 37(4), 749-764. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/3278
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