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A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems

Boundary Value Problems volume 2006, Article number: 37524 (2006) Cite this article

Abstract

We study a final value problem for first-order abstract differential equation with positive self-adjoint unbounded operator coefficient. This problem is ill-posed. Perturbing the final condition, we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions converge if and only if the original problem has a classical solution. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.

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Authors and Affiliations

  1. Laboratoire Equations Differentielles, Département de Mathématiques, Faculté des Sciences, Université Mentouri Constantine, Constantine, 25000, Algeria

    M Denche & S Djezzar

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  1. M Denche
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  2. S Djezzar
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Correspondence to M Denche.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Denche, M., Djezzar, S. A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems. Bound Value Probl 2006, 37524 (2006). https://doi.org/10.1155/BVP/2006/37524

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  • DOI: https://doi.org/10.1155/BVP/2006/37524

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Convergence Rate