Calculation of Multifrequency Impulse Effects on Inhomogeneous Media Using the Lebesgue Integral

In the work on the basis of the Lebesgue integral, a method for accounting for the averaged effect of a multifrequency pulse signal on the state of the medium with fixed initial data is proposed. A multiparameter analysis of the solution of the corresponding system of inhomogeneous differential equations has been carried out, and the asymptotics of the resulting solution with an unlimited increase in the parameters of the medium has been investigated. It is shown that at certain values of the determining parameters in the system, a resonance occurs, in which the amplitude and frequency of oscillations Systems depend on only one parameter and do not depend on the value of other parameters.