Mixed Problem for an Impulsive Parabolic Integro-Differential Equation with Involution and Nonlinear Conditions

IF 0.8 Q2 MATHEMATICS Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI:10.1134/s199508022460078x
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":"4 1","pages":""},"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.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
带卷积和非线性条件的脉冲抛物整微分方程的混合问题
摘要 本文考虑了一个具有退化 kerneland 内卷的脉冲同调抛物型偏积分微分方程。关于空间变量 \(x\) 使用了 Dirichlet 边界值条件,并研究了谱问题。应用傅里叶变量分离法,得到了关于未知函数傅里叶系数的可数非线性函数方程组,证明了可数函数方程组唯一可解性定理。结合使用了连续逼近法和收缩映射法。以傅里叶级数形式得到了脉冲混合问题的唯一解。证明了傅里叶级数的绝对均匀收敛性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
1.50
自引率
42.90%
发文量
127
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.
期刊最新文献
Oscillations of Nanofilms in a Fluid Pressure Diffusion Waves in a Porous Medium Saturated by Three Phase Fluid Effect of a Rigid Cone Inserted in a Tube on Resonant Gas Oscillations Taylor Nearly Columnar Vortices in the Couette–Taylor System: Transition to Turbulence From Texts to Knowledge Graph in the Semantic Library LibMeta
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1