On the stability criteria of solutions of partial differential equations of hyperbolic type

The paper is dedicated to the analysis of Liapunov stability of solutions of systems of linear partial differential equations of hyperbolic type with time-depending coefficients. Investigation of stability is based on the use of Fourier transformation in space variables for the transition from original problem to parametric system of ordinary differentials equations in spectral domain, and the further analysis of solutions of the system with the use of Liapunov transformations and logarithmic norms. An algorithm that enables to obtain criteria of stability of solutions of finite systems of linear hyperbolic equations with time-depending coefficients has been proposed, and also several examples of application of the algorithm for the investigation of stability of solutions of hyperbolic equation and of the system of hyperbolic equations with constant coefficients have been given. The devised algorithm can be used for investigation of dynamical systems that are governed by systems of hyperbolic equations.