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This article is cited in 6 scientific papers (total in 6 papers)
Construction of Eigenfunctions of the Tricomi–Neumann Problem for Equations of Mixed Type with Characteristic Degeneration and Their Application
K. B. Sabitova, S. L. Bibakovab a Academy of Sciences of Bashkortostan
b Sterlitamak State Pedagogical Institute
Abstract:
For the equation of mixed type
$$
L_\alpha u\equiv u_{xx}+yu_{yy}+\alpha u_y+\lambda u=0,
$$
where $0<\alpha<1$ and $\lambda$ is a complex parameter, we obtain eigenvalues in a special domain by the method of separation of variables and construct the system of corresponding eigenfunctions of the Tricomi–Neumann spectral problem. We construct the solution of the Tricomi–Neumann problem as a sum of biorthogonal series.
Received: 14.11.2001
Citation:
K. B. Sabitov, S. L. Bibakova, “Construction of Eigenfunctions of the Tricomi–Neumann Problem for Equations of Mixed Type with Characteristic Degeneration and Their Application”, Mat. Zametki, 74:1 (2003), 76–87; Math. Notes, 74:1 (2003), 70–80
Linking options:
https://www.mathnet.ru/eng/mzm247https://doi.org/10.4213/mzm247 https://www.mathnet.ru/eng/mzm/v74/i1/p76
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Abstract page: | 516 | Full-text PDF : | 253 | References: | 69 | First page: | 1 |
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