Finite Time Stabilization to Zero and Exponential Stability of Quasilinear Hyperbolic Systems

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...

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Bibliographic Details
Published in:Siberian mathematical journal 2023-11, Vol.64 (6), p.1356-1371
Main Author: Lyul’ko, N. A.
Format: Article
Language:English
Subjects:
Asymptotic properties
Boundary conditions
Hyperbolic systems
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446623060101