The completeness of the eigenfunctions of the Tricomi problem for the Lavrent'ev–Bitsadze equation with the Frankl gluing condition

Моисеев, Е. И.; Gulyaev, D. A.

doi:10.1080/10652469.2016.1227806

Cited by 4 publications

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“…Publications on this subject are quite extensive. From the recent publications related to the theme we can note the papers [13,14,19,20,21,22,24]. However in these papers the nonlocal problems were considered in rectangular domains.…”

Section: Introductionmentioning

confidence: 99%

Unique solvability of a nonlocal problem with shift for a parabolic-hyperbolic equation

Urinov

Mamanazarov

2020

Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki

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In this article we study spectral properties of non-local boundaryvalue problem for an equation of parabolic-hyperbolic type. The non-local condition binds the solution values at points on boundaries of the parabolic and hyperbolic parts of the domain with each other. Nonlocal boundary conditions of such type are called Frankl-type conditions. This problem was first formulated by Kal'menov and Sadybekov who proved the unique strong solvability. In this article we investigate one particular case of this problem, for which we show that the problem does not have eigenvalues. 2010 Mathematics Subject Classification. 35M10, 35M12. Key words and phrases. Equation of the mixed type; parabolic-hyperbolic equation; Non-local boundary value problem; Frankl type problem; spectral properties; eigenvalues.

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