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Abstract <p>The initial boundary value problem for Kelvin–Voigt type viscoelasticity model with frame–indifferent constitutive law with regularized objective Yaumann derivative and with infinite memory is considered. A weak solvability of the initial boundary value problem is established. The research is based on the approximation-topological method. For this purpose, we consider an approximating sequence of regularized problems over finite time intervals, for which weak solvability and uniform w.r.t. approximation parameter estimates of weak solutions are established. These estimates allow us to perform passage to the limit in approximating problems.</p>

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Weakly Solvability on an Infinite Interval of the Kelvin–Voigt Model with Smoothed Jaumann Derivative and Memory

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • V. G. Zvyagin,
  • V. P. Orlov

摘要

Abstract

The initial boundary value problem for Kelvin–Voigt type viscoelasticity model with frame–indifferent constitutive law with regularized objective Yaumann derivative and with infinite memory is considered. A weak solvability of the initial boundary value problem is established. The research is based on the approximation-topological method. For this purpose, we consider an approximating sequence of regularized problems over finite time intervals, for which weak solvability and uniform w.r.t. approximation parameter estimates of weak solutions are established. These estimates allow us to perform passage to the limit in approximating problems.