This article is cited in 8 papers

Keldysh problem for mixed type equation with strong characteristic degeneration and singular coefficient

R. M. Safina

Volga Region State Academy of Physical Culture, Sport and Tourism, 35 Universiade Village, Kazan, 420138 Russia

Abstract: For a mixed-type equation of the second kind with a singular coefficient with the use of spectral expansions, we establish a uniqueness criterion for solving the problem with incomplete boundary data. The solution is constructed in the form of the Fourier–Bessel sums. In substantiation of the uniform convergence we establish an estmate on separation from zero of small denominator with the corresponding asymptotic behavior that allowed to substantiate the convergence of the series in the class of regular solutions.

Keywords: mixed type equation, Keldysh problem, singular coefficient, spectral method, uniqueness, Fourier–Bessel series, small denominators.

UDC: 517.957

Received: 14.04.2016

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:8, 46–54

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