Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (4): 1280-1292.doi: 10.1007/s42967-021-00174-x

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Reconstruction of a Heat Equation from One Point Observations

H. Al Attas1, A. Boumenir2   

  1. 1. Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia;
    2. Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA
  • Received:2021-04-20 Revised:2021-07-16 Online:2022-12-20 Published:2022-09-26
  • Supported by:
    Both authors sincerely thank the referees for their comments and KFUPM SB 191035 for its support.

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.

Key words: Inverse problem, Parameter identification, Heat equation

CLC Number: