Studying Volterra Integro-Differential Equations by Methods of the Theory of Operator Semigroups

被引：5

作者：

Rautian, N. A. ^{[1
,2
]}

机构：

[1] Lomonosov Moscow State Univ, Moscow 119991, Russia

[2] Moscow Ctr Fundamental & Appl Math, Moscow 119991, Russia

来源：

DIFFERENTIAL EQUATIONS | 2021年 / 57卷 / 12期

基金：

俄罗斯基础研究基金会;

关键词：

STABILITY;

D O I：

10.1134/S0012266121120120

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study abstract Volterra integro-differential equations with kernels of integral operators represented by Stieltjes integrals. The results are based on an approach related to the study of one-parameter semigroups for linear evolution equations. A method is given for reducing the original initial value problem for a model integro-differential equation with operator coefficients in a Hilbert space to the Cauchy problem for a first-order differential equation in an extended function space. The existence of a contraction C-0-semigroup is proved. The properties of the generator of the semigroup are established based on the properties of the operator function that is the symbol of the original integro-differential equation.

引用

页码：1665 / 1684

页数：20

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