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 Izv. Vyssh. Uchebn. Zaved. Mat., 2015, Number 12, Pages 55–65 (Mi ivm9062)

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

S. N. Sidorov

Chair of Mathematical Analysis, Sterlitamak Branch of the Bashkir State University, 37 Lenin Ave., Sterlitamak, 453103 Russia

Abstract: For mixed type equation in a rectangle, we study boundary-value problems with 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.

Keywords: equation of mixed type, spectral method, existence, uniqueness, stability.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:12, 46–55

UDC: 517.957

Citation: S. N. Sidorov, “Nonlocal problems for an equation of mixed parabolic-hyperbolic type with power degeneration”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 12, 55–65; Russian Math. (Iz. VUZ), 59:12 (2015), 46–55

Citation in format AMSBIB
\Bibitem{Sid15} \by S.~N.~Sidorov \paper Nonlocal problems for an equation of mixed parabolic-hyperbolic type with power degeneration \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2015 \issue 12 \pages 55--65 \mathnet{http://mi.mathnet.ru/ivm9062} \transl \jour Russian Math. (Iz. VUZ) \yr 2015 \vol 59 \issue 12 \pages 46--55 \crossref{https://doi.org/10.3103/S1066369X15120051} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84946423700}