Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 156, Pages 18–29 (Mi into394)  
Gevrey problem for a mixed parabolic equation with singular coefficients

A. O. Mamanazarov

Ferghana State University
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Abstract: In this paper, we examine the unique solvability of the Gevrey problem for a mixed parabolic equation with singular coefficients in a band. We prove the existence and uniqueness of a solution to the problem stated. The uniqueness of a solution is proved by the method of energy integrals and the existence by methods of the theory of Volterra, Fredholm, and singular integral equations.
Keywords: Gevrey problem, mixed parabolic equation, singular coefficient, uniqueness of solution, existence of solution.
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 254, Issue 6, Pages 718–730
DOI: https://doi.org/10.1007/s10958-021-05335-0
Bibliographic databases:
Document Type: Article
UDC: 517.956
MSC: 35A01, 35K20
Language: Russian
Citation: A. O. Mamanazarov, “Gevrey problem for a mixed parabolic equation with singular coefficients”, Mathematical Analysis, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 156, VINITI, Moscow, 2018, 18–29; J. Math. Sci. (N. Y.), 254:6 (2021), 718–730
Citation in format AMSBIB
\Bibitem{Mam18}
\by A.~O.~Mamanazarov
\paper Gevrey problem for a mixed parabolic equation with singular coefficients
\inbook Mathematical Analysis
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 156
\pages 18--29
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into394}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3939193}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 254
\issue 6
\pages 718--730
\crossref{https://doi.org/10.1007/s10958-021-05335-0}
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