TY - JOUR

T1 - Finite Time Stabilization to Zero and Exponential Stability of Quasilinear Hyperbolic Systems

AU - Lyul’ko, N. A.

N1 - This work was carried out within the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0008).

PY - 2023/11

Y1 - 2023/11

N2 - We consider the asymptotic properties of solutions to the mixed problemsfor the quasilinear nonautonomous first-order hyperbolic systems withtwo variables in the case of smoothing boundary conditions.We prove that all smooth solutions to the problem for a decoupled hyperbolic systemstabilize to zero in finite time independently of the initial data.If the hyperbolic system is coupled then we show thatthe zero solution to the quasilinear problem is exponentially stable.

AB - We consider the asymptotic properties of solutions to the mixed problemsfor the quasilinear nonautonomous first-order hyperbolic systems withtwo variables in the case of smoothing boundary conditions.We prove that all smooth solutions to the problem for a decoupled hyperbolic systemstabilize to zero in finite time independently of the initial data.If the hyperbolic system is coupled then we show thatthe zero solution to the quasilinear problem is exponentially stable.

KW - 517.956

KW - exponential stability

KW - first-order quasilinear hyperbolic system

KW - smoothing boundary conditions

KW - stabilization to zero in finite time

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85178929680&origin=inward&txGid=615f3510dfd9e5d83c5b175a7ed5a5bd

UR - https://www.mendeley.com/catalogue/72ed9188-0708-3698-bfc6-cf81827f93b4/

U2 - 10.1134/S0037446623060101

DO - 10.1134/S0037446623060101

M3 - Article

VL - 64

SP - 1356

EP - 1371

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 6

ER -