On a Frankl-type problem for a mixed parabolic-hyperbolic equation
- Authors: Kal’menov T.S.1, Sadybekov M.A.1
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Affiliations:
- Institute of Mathematics and Mathematical Modeling
- Issue: Vol 58, No 2 (2017)
- Pages: 227-231
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171058
- DOI: https://doi.org/10.1134/S0037446617020057
- ID: 171058
Cite item
Abstract
We state a new nonlocal boundary value problem for a mixed parabolic-hyperbolic equation. The equation is of the first kind, i.e., the curve on which the equation changes type is not a characteristic. The nonlocal condition involves points in hyperbolic and parabolic parts of the domain. This problem is a generalization of the well-known Frankl-type problems. Unlike other close publications, the hyperbolic part of the domain agrees with a characteristic triangle. We prove unique solvability of this problem in the sense of classical and strong solutions.
About the authors
T. Sh. Kal’menov
Institute of Mathematics and Mathematical Modeling
Email: sadybekov@math.kz
Kazakhstan, Almaty
M. A. Sadybekov
Institute of Mathematics and Mathematical Modeling
Author for correspondence.
Email: sadybekov@math.kz
Kazakhstan, Almaty