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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 6, Pages 1229–1247
DOI: https://doi.org/10.33048/smzh.2023.64.610 (Mi smj7827) 		 
Finite time stabilization to zero and exponential stability of quasilinear hyperbolic systems

N. A. Lyul'koab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
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DOI: https://doi.org/10.33048/smzh.2023.64.610
Abstract: We consider the asymptotic properties of solutions to the mixed problems for the quasilinear nonautonomous first-order hyperbolic systems with two variables in the case of smoothing boundary conditions. We prove that all smooth solutions to the problem for a decoupled hyperbolic system stabilize to zero in finite time independently of the initial data. If the hyperbolic system is coupled then we show that the zero solution to the quasilinear problem is exponentially stable.
Keywords: first-order quasilinear hyperbolic system, smoothing boundary conditions, stabilization to zero in finite time, exponential stability.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0008
This work was carried out within the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0008).
Received: 20.06.2023
Revised: 20.06.2023
Accepted: 25.09.2023
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 6, Pages 1356–1371
DOI: https://doi.org/10.1134/S0037446623060101
Document Type: Article
UDC: 517.956
MSC: 35R30
Language: Russian
Citation: N. A. Lyul'ko, “Finite time stabilization to zero and exponential stability of quasilinear hyperbolic systems”, Sibirsk. Mat. Zh., 64:6 (2023), 1229–1247; Siberian Math. J., 64:6 (2023), 1356–1371
Citation in format AMSBIB
\Bibitem{Lyu23}
\by N.~A.~Lyul'ko
\paper Finite time stabilization to zero and exponential stability of quasilinear hyperbolic systems
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 6
\pages 1229--1247
\mathnet{http://mi.mathnet.ru/smj7827}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 6
\pages 1356--1371
\crossref{https://doi.org/10.1134/S0037446623060101}
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