Abstract
For a mixed-type equation, we examine the second boundary-value problem and by using the spectral method prove the uniqueness and existence of solutions. The uniqueness criterion is proved based on the completeness property of the biorthogonal system of functions corresponding to the onedimensional spectral problem. A solution of the problem is constructed as the sum of a biorthogonal series.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 137, Mathematical Physics, 2017.
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Gimaltdinova, A.A. Second Boundary-Value Problem for the Lavrent’ev–Bitsadze Equation in a Rectangular Domain with Two Degeneration Lines. J Math Sci 236, 579–593 (2019). https://doi.org/10.1007/s10958-018-4134-0
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DOI: https://doi.org/10.1007/s10958-018-4134-0
Keywords and phrases
- equation of mixed type
- biorthogonal system of functions
- completeness
- existence and uniqueness of solution