Slynko, VitaliiTunc, OsmanAtamas, Ivan2025-05-102025-05-1020240096-30031873-564910.1016/j.amc.2024.1286322-s2.0-85186771547https://doi.org/10.1016/j.amc.2024.128632https://hdl.handle.net/20.500.14720/11036Vitaliy, Slyn'Ko/0000-0002-2321-922XWe study exponential stability of equilibrium in the L (P) -norm (1 < P <= infinity, P not equal 2) of nonlinear 1D systems of hyperbolic equations. A method of construction of Lyapunov functions based on the W. Magnus representation of fundamental solutions of ordinary differential equation (ODE) linear systems is proposed. Sufficient conditions for exponential L (P) -stability (1 < P < infinity, P not equal 2) are obtained and sufficient conditions for exponential L (infinity) -stability are derived by passing to the limit. The obtained results are compared with the well-known results.eninfo:eu-repo/semantics/closedAccessLyapunov FunctionNonlinear Hyperbolic SystemsL-P-NormExponential StabilityMagnus SeriesArticle472Q1Q1WOS:001217613800001