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Direct and inverse boundary value problems for models of stationary reaction–convection–diffusion

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Abstract

Direct and inverse boundary value problems for models of stationary reaction–convection–diffusion are investigated. The direct problem consists in finding a solution of the corresponding boundary value problem for given data on the boundary of the domain of the independent variable. The peculiarity of the direct problem consists in the inhomogeneity and irregularity of mixed boundary data. Solvability and stability conditions are specified for the direct problem. The inverse boundary value problem consists in finding some traces of the solution of the corresponding boundary value problem for given standard and additional data on a certain part of the boundary of the domain of the independent variable. The peculiarity of the inverse problem consists in its ill-posedness. Regularizing methods and solution algorithms are developed for the inverse problem.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    A. I. Korotkii & Yu. V. Starodubtseva

  2. Institute of Mathematics and Computer Science, Ural Federal University, ul. Mira, 19, Yekaterinburg, 620000, Russia

    A. I. Korotkii

Authors
  1. A. I. Korotkii
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  2. Yu. V. Starodubtseva
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Correspondence to A. I. Korotkii.

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Original Russian Text © A.I. Korotkii, Yu.V. Starodubtseva, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 3.

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Korotkii, A.I., Starodubtseva, Y.V. Direct and inverse boundary value problems for models of stationary reaction–convection–diffusion. Proc. Steklov Inst. Math. 291 (Suppl 1), 96–112 (2015). https://doi.org/10.1134/S0081543815090072

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  • DOI: https://doi.org/10.1134/S0081543815090072

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