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Reconstruction of a Heat Equation from One Point Observations

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Abstract

We are concerned with the reconstruction of the heat sink coefficient in a one-dimensional heat equation from the observations of solutions at the same point. This direct method which is based on spectral estimation and asymptotics techniques provides a fast algorithm and also an alternative to the Gelfand-Levitan theory or minimization procedures.

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Acknowledgements

Both authors sincerely thank the referees for their comments and KFUPM SB 191035 for its support.

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Authors and Affiliations

  1. Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    H. Al Attas

  2. Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA

    A. Boumenir

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  1. H. Al Attas
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  2. A. Boumenir
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Correspondence to A. Boumenir.

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Attas, H.A., Boumenir, A. Reconstruction of a Heat Equation from One Point Observations. Commun. Appl. Math. Comput. 4, 1280–1292 (2022). https://doi.org/10.1007/s42967-021-00174-x

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  • DOI: https://doi.org/10.1007/s42967-021-00174-x

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