{"title":"An Inverse Problem for a Hyperbolic Integro-Differential Equation in a Bounded Domain","authors":"J. Sh. Safarov, D. K. Durdiev, A. A. Rakhmonov","doi":"10.1134/s1055134424020068","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the inverse problem of finding the kernel of the integral term in an\nintegro-differential equation. The problem of finding the memory kernel in the wave process is\nreduced to a nonlinear Volterra integral equation of the first kind of convolution type, which is in\nturn reduced under some assumptions to a Volterra integral equation of the second kind. Using\nthe method of contraction mappings, we prove the unique solvability of the problem in the space\nof continuous functions with weighted norms and obtain an estimate of the conditional stability of\nthe solution.\n</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"86 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Advances in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1055134424020068","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the inverse problem of finding the kernel of the integral term in an
integro-differential equation. The problem of finding the memory kernel in the wave process is
reduced to a nonlinear Volterra integral equation of the first kind of convolution type, which is in
turn reduced under some assumptions to a Volterra integral equation of the second kind. Using
the method of contraction mappings, we prove the unique solvability of the problem in the space
of continuous functions with weighted norms and obtain an estimate of the conditional stability of
the solution.
期刊介绍：
Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.
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