This study addresses a mixed problem for a quasilinear system of hyperbolic equations expressed in Riemann invariants, incorporating dissipative nonlinear boundary conditions. A numerical approach is developed through an initial-boundary difference problem utilizing an upwind difference scheme. The stability of nonlinear difference schemes is investigated, with a focus on establishing a sufficient stability criterion based on Lyapunov vector functions. The proposed criterion extends prior theoretical work, where a discrete Lyapunov function was formulated to demonstrate the exponential stability of the steady state for the quasilinear system. Numerical computations for a model problem validate these theoretical findings. The research highlights the potential of adapting the direct Lyapunov method to analyze the stability of nonlinear hyperbolic systems by constructing a positive definite function that exhibits monotonic decay along system solutions.
| Mualliflar | Aloev, R.D., Berdishev, A.S., Nematova, D.E., Алоев, Р.Д., Бердышев, А.С., Нематова, Д.Э. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashr sanasi | 2025-07-27 |
| Son | 3 |
| Betlar | 83-96 |
| Til | Ingliz |
| DOI | 10.71310/pcam.3_67.2025.07 |
DOI: 10.71310/pcam.3_67.2025.07 · Maqolaning asl sahifasi
exponential stability, hyperbolic system, mixed problem, difference scheme, Lyapunov function, экспоненциальная устойчивость, гиперболическая система, смешанная задача, разностная схема, функция Ляпунова
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