A. N. Abdullozhonova, T. K. Yuldashev, A. K. Fayziyev
{"title":"Mixed Problem for an Impulsive Parabolic Integro-Differential Equation with Involution and Nonlinear Conditions","authors":"A. N. Abdullozhonova, T. K. Yuldashev, A. K. Fayziyev","doi":"10.1134/s199508022460078x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we consider an impulsive homogeneous parabolic\ntype partial integro-differential equation with degenerate kernel\nand involution. With respect to spatial variable <span>\\(x\\)</span> is used\nDirichlet boundary value conditions and spectral problem is\nstudied. The Fourier method of separation of variables is applied.\nThe countable system of nonlinear functional equations is obtained\nwith respect to the Fourier coefficients of unknown function.\nTheorem on a unique solvability of countable system of functional\nequations is proved. The method of successive approximations is\nused in combination with the method of contraction mapping. The\nunique solution of the impulsive mixed problem is obtained in the\nform of Fourier series. Absolutely and uniformly convergence of\nFourier series is proved.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s199508022460078x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we consider an impulsive homogeneous parabolic
type partial integro-differential equation with degenerate kernel
and involution. With respect to spatial variable \(x\) is used
Dirichlet boundary value conditions and spectral problem is
studied. The Fourier method of separation of variables is applied.
The countable system of nonlinear functional equations is obtained
with respect to the Fourier coefficients of unknown function.
Theorem on a unique solvability of countable system of functional
equations is proved. The method of successive approximations is
used in combination with the method of contraction mapping. The
unique solution of the impulsive mixed problem is obtained in the
form of Fourier series. Absolutely and uniformly convergence of
Fourier series is proved.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
