Averaging of weakly nonlinear hyperbolic systems with nonuniform integral means (Q1177760)

The author considers the initial value problem for a weakly nonlinear hyperbolic system of first-order partial differential equations. The presence of a small parameter allowed him to divide all the state variables into slow and fast ones and to construct explicitly the time- averaged system. The main result given by the theorem consists in proof of existence and uniqueness solutions for both original and averaged systems, as well as in estimation of closeness of these solutions in uniform metric. In conclusion the connection between author's results and various averaging schemes arising from Bogolyubov and Mitropolski is discussed. References, 12 in number, fully cover the stated problem.