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Abstract <p> For Volterra integro-differential operators in partial derivatives of the second order, the concept of hyperbolicity with respect to a cone is introduced. It is established that the hyperbolicity with respect to a cone is equivalent to the localization of the support of the fundamental solution of the Volterra integro-differential operator in the conjugate cone. The hyperbolicity with respect to a cone of the integro-differential operator of oscillations of a viscoelastic rod with a fractional-exponential relaxation function is proved. </p> <p> <b> DOI</b> 10.1134/S106192082502013X </p>

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Hyperbolic Property of a Linear Volterra Integro-Differential Operator in Problems of Oscillations of a Viscoelastic Rod

  • 期刊论文

  • 发表日期：

    2025年6月1日

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

摘要

Abstract

For Volterra integro-differential operators in partial derivatives of the second order, the concept of hyperbolicity with respect to a cone is introduced. It is established that the hyperbolicity with respect to a cone is equivalent to the localization of the support of the fundamental solution of the Volterra integro-differential operator in the conjugate cone. The hyperbolicity with respect to a cone of the integro-differential operator of oscillations of a viscoelastic rod with a fractional-exponential relaxation function is proved.

DOI 10.1134/S106192082502013X