Email this article Dirichlet–Neumann Problem for Systems of Hyperbolic Equations with Constant Coefficients
- Authors: Ptashnyk B.Y.1,2, Repetylo S.M.2
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Affiliations:
- Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences
- “L’vivs’ka Politekhnika” National University
- Issue: Vol 215, No 1 (2016)
- Pages: 26-35
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237528
- DOI: https://doi.org/10.1007/s10958-016-2819-9
- ID: 237528
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Abstract
In a domain obtained as the Cartesian product of a segment by a circle of unit radius, we investigate a boundary-value problem with Dirichlet–Neumann conditions with respect to the time variable for a system of high-order hyperbolic equations with constant coefficients. We establish the conditions of unique solvability of the problem in the Sobolev spaces and construct its solution in the form of a vector series in a system of orthogonal functions. To establish lower estimates of small denominators encountered in the construction of solutions of the problem, we use the metric approach.
About the authors
B. Yo. Ptashnyk
Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences; “L’vivs’ka Politekhnika” National University
Email: Jade.Santos@springer.com
Ukraine, Lviv; Lviv
S. M. Repetylo
“L’vivs’ka Politekhnika” National University
Email: Jade.Santos@springer.com
Ukraine, Lviv
