Second Boundary-Value Problem for the Lavrent’ev–Bitsadze Equation in a Rectangular Domain with Two Degeneration Lines
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For a mixed-type equation, we examine the second boundary-value problem and by using the spectral method prove the uniqueness and existence of solutions. The uniqueness criterion is proved based on the completeness property of the biorthogonal system of functions corresponding to the onedimensional spectral problem. A solution of the problem is constructed as the sum of a biorthogonal series.
Keywords and phrasesequation of mixed type biorthogonal system of functions completeness existence and uniqueness of solution
AMS Subject Classification35M12
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- 2.L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Surv. Appl. Math., 3, Wiley, New York (1958).Google Scholar
- 13.A. M. Nakhushev, “Uniqueness condition for the Dirichlet problem for a mixed-type equation in a cylindrical domain,” Differ. Uravn., 6, No. 1, 190–191 (1970).Google Scholar
- 14.K. B. Sabitov, “Dirichlet problem for a mixed-type equation in a rectangular domain,” Dokl. Ross. Akad. Nauk, 413, No. 1, 23–26 (2007).Google Scholar
- 16.K. B. Sabitov, G. G. Bikkulova, and A. A. Gimaltdinova, Theory of Mixed-Type Equations with two Degeneration Lines [in Russian], Ufa (2006).Google Scholar
- 21.A. P. Soldatov, “Dirichlet-type problems for the Lavrent’ev–Bitsadze equation, I, II,” Dokl. Ross. Akad. Nauk, 332, No. 6, 696–698 (1993); 333, No. 1, 16–18 (1994).Google Scholar