Electron. J. Differential Equations, Vol. 2018 (2018), No. 65, pp. 1-11.

Spectral properties of a Frankl type problem for parabolic-hyperbolic equations

Makhmud A. Sadybekov, Gulnar Dildabek, Marina B. Ivanova

Abstract:
In this article we study spectral properties of non-local boundary-value 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.

Submitted December 14, 2017. Published March 10, 2018.
Math Subject Classifications: 35M10, 35M12.
Key Words: Equation of the mixed type; parabolic-hyperbolic equation; Non-local boundary value problem; Frankl type problem; spectral properties; eigenvalues.

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Makhmud Sadybekov
Institute of Mathematics and Mathematical Modeling
125 Pushkin str., 050010 Almaty, Kazakhstan
email: sadybekov@math.kz
Gulnar Dildabek
Institute of Mathematics and Mathematical Modeling
125 Pushkin str., 050010 Almaty, Kazakhstan
email: dildabek.g@gmail.com
Marina B. Ivanova
Institute of Mathematics and Mathematical Modeling
125 Pushkin str., 050010 Almaty, Kazakhstan
email: marina-iv@mail.ru

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