Abstract

Abstract Volterra integro-differential equations that are operator models of viscoelasticity problems are investigated. The class of equations under consideration also includes the Gurtin–Pipkin integro-differential equations describing heat propagation in media with memory. As kernels of integral operators, it is possible to use, in particular, sums of decreasing exponents or sums of Rabotnov functions with positive coefficients, which are widely applied in the theory of viscoelasticity and heat propagation theory.

中文翻译：

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半群论方法研究Volterra积分微分方程

摘要

摘要 研究了粘弹性问题算子模型 Volterra 积分微分方程。正在考虑的方程组还包括描述具有记忆的介质中的热传播的 Gurtin-Pipkin 积分微分方程。作为积分算子的核，特别可以使用递减指数之和或具有正系数的拉博特诺夫函数之和，其广泛应用于粘弹性理论和热传播理论中。