Geodesic
Solution of the Tricomi problem for the Lavrentiev-Batsadze equation by spectral analysis
News of the Kabardin-Balkar scientific center of RAS, no. 1 (2002), pp. 84-93.

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In this work, the eigenvalues and corresponding eigenfunctions of the Tricomi-Neumann spectral problem for the Lavrentiev-Bitsadze operator are found. The found system of eigenfunctions is examined for completeness in the domains of ellipticity, hyperbolicity, and in general in the mixed domain. Solutions of the Tricomi-Neumann problems for equations of mixed type with the Lavrentiev-Bitsadze operator are constructed in the form of a sum of biorthogonal series for the eigenfunctions of the spectral problem.
Keywords: Tricomi-Neumann problem, Lavrenev-Bitsadze equation, spectrum 
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K. B. Sabitov; S. L. Khasanova. Solution of the Tricomi problem for the Lavrentiev-Batsadze equation by spectral analysis. News of the Kabardin-Balkar scientific center of RAS, no. 1 (2002), pp. 84-93. http://geodesic.mathdoc.fr/item/IZKAB_2002_1_a14/