{"title":"Well-Posed Solvability of Volterra Integro-Differential Equations Arising in Viscoelasticity Theory","authors":"D. V. Georgievskii, N. A. Rautian","doi":"10.1134/s0012266124040098","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We discuss the well-posed solvability and exponential stability of solutions of abstract\nintegro-differential equations where the kernels of integral operators are of general type and lie in\nthe space of functions integrable on the positive half-line. The abstract integro-differential\nequations studied in the present paper are operator models of viscoelasticity theory problems. The\nproposed approach to the study of these integro-differential equations is related to an application\nof semigroup theory and can also be used to study other integro-differential equations containing\nintegral terms of the Volterra convolution type.\n</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"30 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124040098","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We discuss the well-posed solvability and exponential stability of solutions of abstract
integro-differential equations where the kernels of integral operators are of general type and lie in
the space of functions integrable on the positive half-line. The abstract integro-differential
equations studied in the present paper are operator models of viscoelasticity theory problems. The
proposed approach to the study of these integro-differential equations is related to an application
of semigroup theory and can also be used to study other integro-differential equations containing
integral terms of the Volterra convolution type.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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