FINITE VELOCITY OF PROPAGATION OF PERTURBATIONS FOR A ONE-DIMENSIONAL WAVE INTEGRO-DIFFERENTIAL EQUATION WITH A FRACTIONAL-EXPONENTIAL MEMORY FUNCTION

The paper studies a Volterra integro-differential equation, the main part of which is a one-dimensional wave equation perturbed by an integral operator of the Volterra convolution type (wave equation with memory). The kernel function of the integral operator is a sum of fractional exponential functions (Rabotnov functions) with positive coefficients. The issue of the influence of the integral operator on the velocity of propagation of disturbances in the initial value problem for the wave equation with memory is studied. The Volterra integro-differential equation under study describes oscillations of a one-dimensional viscoelastic rod, as well as the process of heat propagation in media with memory (Gurtin–Pipkin equation).