DOI: 10.12732/ijam.v38i4.2
REFINED STABILITY AND
CONVERGENCE FOR INVERSE
PARABOLIC CAUCHY PROBLEMS
VIA SPECTRAL REGULAR CONTROL
Khaled Bessila1,*, Ali Abdessemed1
1Applied Mathematics and Modeling Laboratory, Constantine 1 - Brothers Mentouri University, Constantine - 25017, ALGERIA
Abstract. In this paper, we address the inverse problem of reconstructing the initial condition for a non-homogeneous parabolic equation from a prescribed final state. This inverse Cauchy problem is well known to be severely ill-posed, with solutions that may not exist or fail to depend continuously on the final data. We propose a novel regularization approach that introduces a controlled perturbation of the final value problem to overcome these difficulties. The proposed method yields significantly improved stability and convergence rates, surpassing classical Holder-type and logarithmic-type estimates presented in previous studies. In particular, we derive new sharp uniform bounds and error estimates, highlighting the effectiveness of our approach in enhancing the stability of the inversion process.
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to cite this paper?
DOI: 10.12732/ijam.v38i4.2
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 4
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