Abstract:
Non-local boundary problem for the axisymmetric Helmholtz equation is explored. The uniqueness of the solution is proved by the spectral method. The conditions of solvability are found. The solution of the problem is constructed in the form of the biorthogonal series.
Citation:
A. A. Abashkin, “On one non-local problem for axisymmetric Helmholtz equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 3(24) (2011), 26–34
\Bibitem{Aba11}
\by A.~A.~Abashkin
\paper On one non-local problem for axisymmetric Helmholtz equation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 3(24)
\pages 26--34
\mathnet{http://mi.mathnet.ru/vsgtu852}
\crossref{https://doi.org/10.14498/vsgtu852}
Linking options:
https://www.mathnet.ru/eng/vsgtu852
https://www.mathnet.ru/eng/vsgtu/v124/p26
This publication is cited in the following 3 articles:
T. G. Ergashev, Z. R. Tulakova, “A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain”, Russian Math. (Iz. VUZ), 66:7 (2022), 51–63
A. A. Abashkin, “Solving one boundary-value problem for mixed type equation with two singular lines with the use of spectral method”, Russian Math. (Iz. VUZ), 60:2 (2016), 1–6
A. A. Abashkin, “Nelokalnaya zadacha dlya uravneniya smeshannogo tipa s singulyarnym koeffitsientom v oblasti,
giperbolicheskaya chast kotoroi — vertikalnaya polupolosa”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 3(36) (2014), 7–20
Citation in format AMSBIB
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