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.
Show me the PDF file (222 KB), TEX file for this article.
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Makhmud Sadybekov Institute of Mathematics and Mathematical Modeling 125 Pushkin str., 050010 Almaty, Kazakhstan email: sadybekov@math.kz |
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Gulnar Dildabek Institute of Mathematics and Mathematical Modeling 125 Pushkin str., 050010 Almaty, Kazakhstan email: dildabek.g@gmail.com |
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Marina B. Ivanova Institute of Mathematics and Mathematical Modeling 125 Pushkin str., 050010 Almaty, Kazakhstan email: marina-iv@mail.ru |
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