Blow-up Results for Fractional Evolution Problems with Nonlocal Diffusion
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- 作者：Mohamed Jleli ; Mokhtar Kirane ; Bessem Samet
- 关键词：Nonlocal diffusion ; fractional derivative ; nonexistence ; global solution
- 刊名：Mediterranean Journal of Mathematics
- 出版年：2016
- 出版时间：October 2016
- 年：2016
- 卷：13
- 期：5
- 页码：3513-3523
- 全文大小：524 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Birkh盲user Basel
- ISSN：1660-5454
- 卷排序：13
文摘
We provide a sufficient condition for the nonexistence of global positive solutions to the nonlocal fractional diffusion problem$$\left\{\begin{array}{ll}D_{0|t}^\alpha (u-u_0)(x,t)= J*u(x,t)-u(x,t)+u^p(x,t),\quad (x,t)\in \mathbb{R}^N \times (0,\infty),\\ u(x,0)=u_0(x), \quad x\in \mathbb{R}^N,\end{array}\right.$$where \({D_{0|t}^\alpha}\) denotes the Riemann-Liouville fractional derivative of order \({\alpha \in (0, 1)}\), J is a nonnegative function defined in \({\mathbb{R}^N}\) and p > 1. Next, we consider the case of a nonlocal fractional diffusion system. The proofs of our results make use of a duality argument.KeywordsNonlocal diffusionfractional derivativenonexistenceglobal solutionMathematics Subject Classification35A0135A2326A3334K37References1.De Masi A., Orlandi E., Presutti G., Triolo L.: Glauber evolution with Kac potentials. I. Mesoscopic and macroscopic limits, interface dynamics. 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Appl. 428, 227–237 (2015)MathSciNetCrossRefMATHGoogle ScholarCopyright information© Springer International Publishing 2016Authors and AffiliationsMohamed Jleli1Mokhtar Kirane23Bessem Samet1Email author1.Department of Mathematics, College of ScienceKing Saud UniversityRiyadhSaudi Arabia2.LaSIE, Faculté des, Sciences et TechnologiesUniversité de La RochelleLa RochelleFrance3.NAAM Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia About this article CrossMark Print ISSN 1660-5446 Online ISSN 1660-5454 Publisher Name Springer International Publishing About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s00009-016-0700-1_Blow-up Results for Fractional Evo", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s00009-016-0700-1_Blow-up Results for Fractional Evo", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. 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