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Reconstruction of the right-hand side of a parabolic equation

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Abstract

A parabolic equation under the influence of external perturbations is considered. It is assumed that the solutions to this equation are measured (possibly with errors). The problem of construction of differential equations for estimation (reconstruction) of perturbations using the measured data is discussed. Differential equations of the auxiliary system whose right-hand sides are approximations of the unknown input are derived.

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Authors and Affiliations

  1. Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia

    M. M. Lavrent’ev

  2. Institute of Mathematics and Mechanics, Ural Division, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russia

    V. I. Maksimov

Authors
  1. M. M. Lavrent’ev
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  2. V. I. Maksimov
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Correspondence to M. M. Lavrent’ev.

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Original Russian Text © M.M. Lavrent’ev, V.I. Maksimov, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 4, pp. 674–680.

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Lavrent’ev, M.M., Maksimov, V.I. Reconstruction of the right-hand side of a parabolic equation. Comput. Math. and Math. Phys. 48, 641–647 (2008). https://doi.org/10.1134/S0965542508040118

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