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Abstract <p> The paper studies a Volterra integro-differential equation, the main part of which is aone-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 the sum offractional exponential functions (Rabotnov functions) with positive coefficients. The influence ofthe integral operator on the velocity of propagation of disturbances in the initial value problem forthe wave equation with memory is studied. The Volterra integro-differential equation under studydescribes oscillations of a one-dimensional viscoelastic rod, as well as the process of heatpropagation in media with memory (Gurtin–Pipkin equation).</p>

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Finite Velocity of Propagation of Perturbations for a One-Dimensional Wave Integro-Differential Equation with a Fractional-Exponential Memory Function

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • D. V. Georgievskii,
  • N. A. Rautian

摘要

Abstract

The paper studies a Volterra integro-differential equation, the main part of which is aone-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 the sum offractional exponential functions (Rabotnov functions) with positive coefficients. The influence ofthe integral operator on the velocity of propagation of disturbances in the initial value problem forthe wave equation with memory is studied. The Volterra integro-differential equation under studydescribes oscillations of a one-dimensional viscoelastic rod, as well as the process of heatpropagation in media with memory (Gurtin–Pipkin equation).