Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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POLLUTION DETECTION FOR THE SINGULAR LINEAR PARABOLIC EQUATION

  • IQBAL M. BATIHA (Department of Mathematics, Al Zaytoonah University of Jordan) ;
  • IMAD REZZOUG (Department of Mathematics and Computer Science, University of Larbi Ben M'hidi) ;
  • TAKI-EDDINE OUSSAEIF (Department of Mathematics and Computer Science, University of Larbi Ben M'hidi) ;
  • ADEL OUANNAS (Department of Mathematics and Computer Science, University of Larbi Ben M'hidi) ;
  • IQBAL H. JEBRIL (Department of Mathematics, Al Zaytoonah University of Jordan)
  • Received : 2022.10.08
  • Accepted : 2022.12.10
  • Published : 2023.05.30
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Abstract

In this work, we are concerned by the problem of identification of noisy terms which arise in singular problem as for remote sensing problems, and which are modeled by a linear singular parabolic equation. For the reason of missing some data that could be arisen when using the traditional sentinel method, the later will be changed by a new sentinel method for attaining the same purpose. Such new method is a particular least square-like method which permits one to distinguish between the missing terms and the pollution terms. In particular, a sentinel method will be given here in its more realistic setting for singular parabolic problems, where in this case, the observation and the control have their support in different open sets. The problem of finding a new sentinel is equivalent to finding singular optimality system of the least square control for the parabolic equation that we solve.

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