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Nonlocal problems for an equation of mixed parabolic-hyperbolic type with power degeneration

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Abstract

Formixed type equation in a rectangle, we study boundary-value problemswith nonlocal boundary condition that connects the values of the sought-for solution and its derivative along the normal at upper and lower bases of the rectangle which belong to different types of studied equation. By the method of spectral analysis we establish criteria of uniqueness of solutions that are constructed in the form of the sum of the Fourier series. We establish the stability of solutions for a nonlocal condition.

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Authors and Affiliations

  1. Sterlitamak Branch of the Bashkir State University, pr. Lenin 37, Sterlitamak, 453103, Russia

    S. N. Sidorov

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  1. S. N. Sidorov
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Correspondence to S. N. Sidorov.

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Original Russian Text © S.N. Sidorov, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 12, pp. 55–65.

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Sidorov, S.N. Nonlocal problems for an equation of mixed parabolic-hyperbolic type with power degeneration. Russ Math. 59, 46–55 (2015). https://doi.org/10.3103/S1066369X15120051

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  • DOI: https://doi.org/10.3103/S1066369X15120051

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