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Continuous Dependence on Modeling in Banach Space Using a Logarithmic Approximation

In: Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Author

Listed:
  • Matthew Fury

    (Penn State Abington)

  • Beth Campbell Hetrick

    (Gettysburg College)

  • Walter Huddell

    (Eastern University)

Abstract

We prove regularization for certain ill-posed problems in Banach space by considering small changes in the model. The problems are of the form d u ∕ d t = A u , 0 ≤ t 0 which approximates A in some sense as the parameter β tends to zero. The particular logarithmic approximation we apply originates from a modified quasi-reversibility method recently introduced by Boussetila and Rebbani.

Suggested Citation

  • Matthew Fury & Beth Campbell Hetrick & Walter Huddell, 2016. "Continuous Dependence on Modeling in Banach Space Using a Logarithmic Approximation," Springer Books, in: Jacques Bélair & Ian A. Frigaard & Herb Kunze & Roman Makarov & Roderick Melnik & Raymond J. Spiteri (ed.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pages 653-663, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30379-6_59
    DOI: 10.1007/978-3-319-30379-6_59
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