Mathematical modeling of wave propagation in viscoelastic media with the fractional Zener model

The question of interest for the presented study is the mathematical modeling of wave propagation in dissipative media. The generalized fractional Zener model in the case of dimension d (d=1,2,3) is considered. This work is devoted to the mathematical analysis of such model: existence and uniqueness of the strong and weak solution and energy decay result which guarantees the wave dissipation. The existence of the weak solution is shown using a priori estimates for solutions which are also presented.

Propagation of video pulse signals in dissipative media

The results of the numerical solution of the problem of propagation of an electromagnetic video pulse signal of nanosecond duration in a dissipative medium are presented for use in the deep georadar data interpretation. Based on the developed scheme for integrating Maxwell's equations, the results of numerical modeling of the propagation of electromagnetic pulses of various shapes without approximations, usually used in the traditional solution of GPR problems, including the separation of temporal and spatial variables of the electromagnetic field and neglect of the rapid field change in comparison with the processes occurring in the medium, are obtained. The influence of the pulse shape on the shape of the electromagnetic echo signal is considered for various models of the medium close to real conditions, including those with a gradient change in electrical conductivity and permittivity. The influence of the distribution of electrical conductivity of the medium is studied.