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Regularization of Nonhomogeneous Ill-Posed Parabolic Cauchy Problems via a Two-Parameter Method With Stability Estimates

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  • Faiza Boulham
  • Nihed Teniou

Abstract

This study aims to propose a regularization method for an ill-posed Cauchy problem involving an unbounded linear operator in a Hilbert space, in order to obtain a stable approximate solution together with error estimates. The main idea of the method developed in this study is to simultaneously perturb both the right-hand side of the equation ft and the final data g. Finally, a numerical example demonstrates the effectiveness of the proposed method.

Suggested Citation

  • Faiza Boulham & Nihed Teniou, 2026. "Regularization of Nonhomogeneous Ill-Posed Parabolic Cauchy Problems via a Two-Parameter Method With Stability Estimates," Journal of Mathematics, Hindawi, vol. 2026, pages 1-22, March.
    • Handle: RePEc:hin:jjmath:8721457
    DOI: 10.1155/jom/8721457
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