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Determining the Thermal Mode Setting Parameters Based on Output Data

  • PARTIAL DIFFERENTIAL EQUATIONS
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Abstract

We consider a mathematical model of the process of heating a cylindrical domain by embedded heat sources under the assumption that heat exchange with the environment occurs on the lateral surface in accordance with Newton’s law. The heating process is controlled by embedding or removing cooling elements. We prove that the time history of the volume of the embedded cooling elements can be uniquely reconstructed based on the output power, which is a function of time representing a weighted average temperature in the domain.

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Authors and Affiliations

  1. National University of Uzbekistan, Tashkent, 100174, Uzbekistan

    Sh. A. Alimov

  2. Andijan State University, Andijan, 170100, Uzbekistan

    N. M. Komilov

Authors
  1. Sh. A. Alimov
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  2. N. M. Komilov
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Corresponding authors

Correspondence to Sh. A. Alimov or N. M. Komilov.

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Translated by V. Potapchouck

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Alimov, S.A., Komilov, N.M. Determining the Thermal Mode Setting Parameters Based on Output Data. Diff Equat 58, 21–35 (2022). https://doi.org/10.1134/S0012266122010049

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  • DOI: https://doi.org/10.1134/S0012266122010049

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