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Matematicheskie Zametki, 2023, Volume 114, Issue 5, Pages 702–720
DOI: https://doi.org/10.4213/mzm13738 (Mi mzm13738) 		 
A Mixed Problem for a Class of Second-Order Nonlinear Hyperbolic Systems with Dirichlet and Poincaré Boundary Conditions

O. M. Dzhokhadzeab, S. S. Kharibegashvilibc, N. N. Shavlakadzeb

a Tbilisi Ivane Javakhishvili State University
b Andrea Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University
c Georgian Technical University, Tbilisi
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DOI: https://doi.org/10.4213/mzm13738
Abstract: For a certain class of second-order hyperbolic systems, a mixed problem with Dirichlet and Poincaré boundary conditions is studied. In the linear case, an explicit representation of a soultion of this problem is given and questions related to its uniqueness and existence are studied depending on the character of nonlinearities in the system.
Keywords: semilinear hyperbolic system, mixed problem, a priori estimate, Laplace invariants.
Funding agency Grant number
Shota Rustaveli National Science Foundation FR-21-7307
This work was financially supported by the Shota Rustaveli National Science Foundation (grant no. FR-21-7307).
Received: 23.09.2022
Revised: 10.12.2022
English version:
Mathematical Notes, 2023, Volume 114, Issue 5, Pages 748–762
DOI: https://doi.org/10.1134/S000143462311010X
Bibliographic databases:
Document Type: Article
UDC: 517.956.3
MSC: 35L53
Language: Russian
Citation: O. M. Dzhokhadze, S. S. Kharibegashvili, N. N. Shavlakadze, “A Mixed Problem for a Class of Second-Order Nonlinear Hyperbolic Systems with Dirichlet and Poincaré Boundary Conditions”, Mat. Zametki, 114:5 (2023), 702–720; Math. Notes, 114:5 (2023), 748–762
Citation in format AMSBIB
\Bibitem{DzhKhaSha23}
\by O.~M.~Dzhokhadze, S.~S.~Kharibegashvili, N.~N.~Shavlakadze
\paper A Mixed Problem for a Class of Second-Order Nonlinear Hyperbolic Systems with Dirichlet and Poincar\'e Boundary Conditions
\jour Mat. Zametki
\yr 2023
\vol 114
\issue 5
\pages 702--720
\mathnet{http://mi.mathnet.ru/mzm13738}
\crossref{https://doi.org/10.4213/mzm13738}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4716480}
\transl
\jour Math. Notes
\yr 2023
\vol 114
\issue 5
\pages 748--762
\crossref{https://doi.org/10.1134/S000143462311010X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85187663131}
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