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

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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.

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Funding

This work was carried out within the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0008).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    N. A. Lyul’ko

  2. Novosibirsk State University, Novosibirsk, Russia

    N. A. Lyul’ko

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  1. N. A. Lyul’ko
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Correspondence to N. A. Lyul’ko.

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As author of this work, I declare that I have no conflicts of interest.

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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 6, pp. 1229–1247. https://doi.org/10.33048/smzh.2023.64.610

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Lyul’ko, N.A. Finite Time Stabilization to Zero and Exponential Stability of Quasilinear Hyperbolic Systems. Sib Math J 64, 1356–1371 (2023). https://doi.org/10.1134/S0037446623060101

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  • DOI: https://doi.org/10.1134/S0037446623060101

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