Geodesic
Dirichlet problem for Pulkin’s equation in a rectangular domain
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2014), pp. 91-101

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In the given article for the mixed-type equation with a singular coefficient the first boundary value problem is studied. On the basis of property of completeness of the system of own functions of one-dimensional spectral problem the criterion of uniqueness is established. The solution the problem is constructed as the sum of series of Fourier–Bessel. At justification of convergence of a row there is a problem of small denominators. In connection with that the assessment about apartness of small denominator from zero with the corresponding asymptotic which allows to prove the convergence of the series constructed in a class of regular solutions under some restrictions is given.
Keywords: equation of a mixed type, Dirichlet problem, spectral method, series of Fourier–Bessel, uniqueness
Mots-clés : existence. 
@article{VSGU_2014_10_a9,
     author = {R. M. Safina},
     title = {Dirichlet problem for {Pulkin{\textquoteright}s} equation in a rectangular domain},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {91--101},
     publisher = {mathdoc},
     number = {10},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2014_10_a9/}
}
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R. M. Safina. Dirichlet problem for Pulkin’s equation in a rectangular domain. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2014), pp. 91-101. http://geodesic.mathdoc.fr/item/VSGU_2014_10_a9/