Abstract
We obtain sufficient conditions for the solvability of the Dirichlet problem for a mixed-type equation of the second kind in a rectangular domain. The solution is represented by a convergent series constructed from the problem data. Some cases of nonuniqueness of the solution are described.
Similar content being viewed by others
References
Khairullin, R.S., On the Dirichlet problem for a mixed-type equation of the second kind with strong degeneration, Differ. Equations, 2013, vol. 49, no. 4, pp. 510–516.
Abramowitz, M. and Stegun, I.A., Handbook on Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Washington: U.S.Government, 1964. Translated under the title Spravochnik po spetsial’nym funktsiyam, Moscow: Nauka, 1979.
Sabitov, K.B., Dirichlet problem for mixed-type equations in a rectangular domain, Dokl. Math., 2007, vol. 75, no. 2, pp. 193–196.
Sabitov, K.B. and Suleimanova, A.Kh., The Dirichlet problem for a mixed-type equation with characteristic degeneration in a rectangular domain, Russ. Math., 2009, vol. 53, no. 11, pp. 37–45.
Safina, R.M., Keldysh problem for a mixed-type equation of the second kind with the Bessel operator, Differ. Equations, 2015, vol. 51, no. 10, pp. 1347–1359.
Tikhonov, A.N. and Samarskii, A.A., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Nauka, 1972.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © R.S. Khairullin, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 5, pp. 684–692.
Rights and permissions
About this article
Cite this article
Khairullin, R.S. Solvability of the Dirichlet problem for a mixed-type equation of the second kind. Diff Equat 53, 677–685 (2017). https://doi.org/10.1134/S0012266117050111
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0012266117050111