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<p>The properties of a&#xa0;linear operator, which is the generator of a&#xa0;semigroup generated by Volterra integro-differential equations in Hilbert spaces, are investigated. The integro-differential equations under consideration can be implemented as partial integro-differential equations arising in the theory of viscoelasticity, the theory of heat propagation in media with memory and having a&#xa0;number of other important applications. The results obtained in the work can be used to study the behavior and obtain estimates of solutions of Volterra integro-differential equations.</p>

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INVESTIGATION OF THE GENERATORS OF SEMIGROUPS ASSOCIATED WITH VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • V. V. Vlasov,
  • N. A. Rautian

摘要

The properties of a linear operator, which is the generator of a semigroup generated by Volterra integro-differential equations in Hilbert spaces, are investigated. The integro-differential equations under consideration can be implemented as partial integro-differential equations arising in the theory of viscoelasticity, the theory of heat propagation in media with memory and having a number of other important applications. The results obtained in the work can be used to study the behavior and obtain estimates of solutions of Volterra integro-differential equations.