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Numerical Solution to Inverse Problems of Recovering Special-Type Source of a Parabolic Equation

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Mathematical Analysis in Interdisciplinary Research

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 179))

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Abstract

The chapter investigates inverse problems of recovering a source of a special type of parabolic equation with initial and boundary conditions. The specificity of these problems is that the identifiable parameters depend on only space or time variable and are factors of the coefficients of the right-hand side of the equation. By applying the method of lines, the problems are reduced to parametric inverse problems with respect to ordinary differential equations. A special type of representation of the solution is proposed to solve them. The most important in this work is that the proposed approach to the numerical solution to the investigated inverse problems of identifying the coefficients does not require to construct any iterative procedure. The results of numerical experiments conducted on test problems are provided.

AMS Subject Classifications

35R30; 35K20; 65N40; 65N21, 65L09, 34A55

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Author information

Authors and Affiliations

  1. Institute of Control Systems of Azerbaijan NAS, Baku, Azerbaijan

    K. R. Aida-zade & A. B. Rahimov

  2. Institute of Control Systems of Azerbaijan NAS, Baku, Azerbaijan

    K. R. Aida-zade

Authors
  1. K. R. Aida-zade
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  2. A. B. Rahimov
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Editor information

Editors and Affiliations

  1. Department of Environmental Sciences, University of Thessaly, Larissa, Greece

    Ioannis N. Parasidis

  2. Department of Environmental Sciences, University of Thessaly, Larissa, Greece

    Efthimios Providas

  3. Department of Mathematics Zografou Campus, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Aida-zade, K.R., Rahimov, A.B. (2021). Numerical Solution to Inverse Problems of Recovering Special-Type Source of a Parabolic Equation. In: Parasidis, I.N., Providas, E., Rassias, T.M. (eds) Mathematical Analysis in Interdisciplinary Research. Springer Optimization and Its Applications, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-030-84721-0_6

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