A Numerical Study on the Lyapunov Stability of Solutions to a Quasilinear Hyperbolic System

This paper addresses the numerical study of the exponential stability of the initial-boundary value problem for a quasilinear system of hyperbolic equations expressed in Riemann invariants, with dissipative nonlinear boundary conditions. To numerically solve this initial-boundary value problem, we propose utilizing a difference scheme based on an upwind method. The discrete Lyapunov function is presented as a tool for the numerical solution of the initial-boundary value difference problem, and its effectiveness is supported through various examples. Furthermore, the conditions outlined in the theorem concerning the exponential stability of the stationary state of a quasilinear system are numerically analyzed.

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