Abstract

The well-posedness of initial value problems for abstract integrodifferential equations with unbounded operator coefficients in Hilbert spaces is studied, and spectral analysis of the operator functions that are the symbols of these equations is performed. The equations under consideration are an abstract form of linear partial integrodifferential equations arising in viscoelasticity theory, which have a number of other important applications. Results concerning the well-posedness of these integrodifferential equations in weighted Sobolev spaces of vector functions defined on the positive half-line with values in a Hilbert space are obtained. The localization and structure of the spectrum of the operator functions that are the symbols of these equations are established.

中文翻译：

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遗传力学积分微分方程的适定性和谱分析

摘要

研究了希尔伯特空间中具有无穷算子系数的抽象积分微分方程初值问题的适定性，并对作为这些方程符号的算子函数进行了频谱分析。所考虑的方程是粘弹性理论中出现的线性局部积分微分方程的抽象形式，具有许多其他重要应用。获得了关于这些积分微分方程在正半线上定义的矢量函数的加权Sobolev空间中具有希尔伯特空间中的值的适定性的结果。建立了作为这些方程式符号的算子函数的频谱的局部化和结构。