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Inverse problem for degenerate parabolic-hyperbolic equation with nonlocal boundary condition

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Abstract

For a mixed type equation with a power-law degeneration we consider the inverse problem on finding an unknown right side. We establish a uniqueness criterion of solution to the problem with a nonlocal condition that connects the normal derivative of the sought-for solution, which belongs to different types of studied equations. The solution is constructed in the form of sums of a series in eigenfunctions of the corresponding one-dimensional spectral problem. We also prove stability of the solution to the nonlocal boundary condition.

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Authors and Affiliations

  1. Institute of Applied Research of Bashkortostan Republic, ul. Odesskaya 68, Sterlitamak, 453103, Russia

    K. B. Sabitov

  2. Sterlitamak Branch of the Bashkir State University, pr. Lenina 37, Sterlitamak, 453103, Russia

    S. N. Sidorov

Authors
  1. K. B. Sabitov
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  2. S. N. Sidorov
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Correspondence to K. B. Sabitov.

Additional information

Original Russian Text © K.B. Sabitov, S.N. Sidorov, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 1, pp. 46–59.

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Sabitov, K.B., Sidorov, S.N. Inverse problem for degenerate parabolic-hyperbolic equation with nonlocal boundary condition. Russ Math. 59, 39–50 (2015). https://doi.org/10.3103/S1066369X15010041

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  • DOI: https://doi.org/10.3103/S1066369X15010041

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