分数阶Volterra积分微分拟抛物型方程的初值问题

IF 2.6 4区 数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY
N. Phuong, N. Tuan, Devendra Kumar, N. Tuan
{"title":"分数阶Volterra积分微分拟抛物型方程的初值问题","authors":"N. Phuong, N. Tuan, Devendra Kumar, N. Tuan","doi":"10.1051/MMNP/2021015","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate a initial value problem for the Caputo time-fractional pseudo-parabolic equations with fractional Laplace operator of order 0 < ν ≤ 1 and the nonlinear memory source term. For 0 < ν < 1, the problem will be considered on a bounded domain of ℝd. By some Sobolev embeddings and the properties of the Mittag-Leffler function, we will give some results on the existence and the uniqueness of mild solution for problem (1.1) below. When ν = 1, we will introduce some Lp − Lq estimates, and based on them we derive the global existence of a mild solution in the whole space ℝd.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"Initial value problem for fractional Volterra integrodifferential pseudo-parabolic equations\",\"authors\":\"N. Phuong, N. Tuan, Devendra Kumar, N. Tuan\",\"doi\":\"10.1051/MMNP/2021015\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we investigate a initial value problem for the Caputo time-fractional pseudo-parabolic equations with fractional Laplace operator of order 0 < ν ≤ 1 and the nonlinear memory source term. For 0 < ν < 1, the problem will be considered on a bounded domain of ℝd. By some Sobolev embeddings and the properties of the Mittag-Leffler function, we will give some results on the existence and the uniqueness of mild solution for problem (1.1) below. When ν = 1, we will introduce some Lp − Lq estimates, and based on them we derive the global existence of a mild solution in the whole space ℝd.\",\"PeriodicalId\":18285,\"journal\":{\"name\":\"Mathematical Modelling of Natural Phenomena\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2021-03-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Modelling of Natural Phenomena\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1051/MMNP/2021015\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICAL & COMPUTATIONAL BIOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Modelling of Natural Phenomena","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/MMNP/2021015","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICAL & COMPUTATIONAL BIOLOGY","Score":null,"Total":0}
引用次数: 11

摘要

在本文中,我们研究了具有阶0<Γ≤1的分数阶拉普拉斯算子和非线性记忆源项的Caputo时间分数阶伪抛物型方程的一个初值问题。对于0<Γ<1,该问题将在ℝd.通过一些Sobolev嵌入和Mittag-Leffler函数的性质,我们将给出以下问题(1.1)的温和解的存在性和唯一性的一些结果。当Γ=1时,我们将引入一些Lp−Lq估计,并基于它们导出整个空间中温和解的全局存在性ℝd
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Initial value problem for fractional Volterra integrodifferential pseudo-parabolic equations
In this paper, we investigate a initial value problem for the Caputo time-fractional pseudo-parabolic equations with fractional Laplace operator of order 0 < ν ≤ 1 and the nonlinear memory source term. For 0 < ν < 1, the problem will be considered on a bounded domain of ℝd. By some Sobolev embeddings and the properties of the Mittag-Leffler function, we will give some results on the existence and the uniqueness of mild solution for problem (1.1) below. When ν = 1, we will introduce some Lp − Lq estimates, and based on them we derive the global existence of a mild solution in the whole space ℝd.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Mathematical Modelling of Natural Phenomena
Mathematical Modelling of Natural Phenomena MATHEMATICAL & COMPUTATIONAL BIOLOGY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
CiteScore
5.20
自引率
0.00%
发文量
46
审稿时长
6-12 weeks
期刊介绍: The Mathematical Modelling of Natural Phenomena (MMNP) is an international research journal, which publishes top-level original and review papers, short communications and proceedings on mathematical modelling in biology, medicine, chemistry, physics, and other areas. The scope of the journal is devoted to mathematical modelling with sufficiently advanced model, and the works studying mainly the existence and stability of stationary points of ODE systems are not considered. The scope of the journal also includes applied mathematics and mathematical analysis in the context of its applications to the real world problems. The journal is essentially functioning on the basis of topical issues representing active areas of research. Each topical issue has its own editorial board. The authors are invited to submit papers to the announced issues or to suggest new issues. Journal publishes research articles and reviews within the whole field of mathematical modelling, and it will continue to provide information on the latest trends and developments in this ever-expanding subject.
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信