Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions

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dc.contributor.authorZhang, Jiancs
dc.contributor.authorRadulescu, Vicentiucs
dc.contributor.authorYang, Minbocs
dc.contributor.authorZhou, Jiazhengcs
dc.coverage.issue1cs
dc.coverage.volume37cs
dc.date.accessioned2025-05-30T10:56:11Z
dc.date.available2025-05-30T10:56:11Z
dc.date.issued2025-03-26cs
dc.description.abstractIn this paper, we study the initial boundary value problem for the nonlocal parabolic equation with the Hardy-Littlewood-Sobolev critical exponent on a bounded domain. We are concerned with the long time behaviors of solutions when the initial energy is low, critical or high. More precisely, by using the modified potential well method, we obtain global existence and blow-up of solutions when the initial energy is low or critical, and it is proved that the global solutions are classical. Moreover, we obtain an upper bound of blow-up time for J(mu)(u0) < 0 and decay rate of H-0(1) and L-2-norm of the global solutions. When the initial energy is high, we derive some sufficient conditions for global existence and blow-up of solutions. In addition, we are going to consider the asymptotic behavior of global solutions, which is similar to the Palais-Smale (PS for short) sequence of stationary equation.en
dc.formattextcs
dc.format.extent687-725cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationJournal of Dynamics and Differential Equations. 2025, vol. 37, issue 1, p. 687-725.en
dc.identifier.doi10.1007/s10884-023-10278-ycs
dc.identifier.issn1572-9222cs
dc.identifier.orcid0000-0003-4615-5537cs
dc.identifier.other185760cs
dc.identifier.researcheridA-1503-2012cs
dc.identifier.scopus35608668800cs
dc.identifier.urihttps://hdl.handle.net/11012/251189
dc.language.isoencs
dc.publisherSpringer Naturecs
dc.relation.ispartofJournal of Dynamics and Differential Equationscs
dc.relation.urihttps://link.springer.com/article/10.1007/s10884-023-10278-ycs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1572-9222/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectNonlocal parabolic equationen
dc.subjectHardy-Littlewood-Sobolev critical exponenten
dc.subjectGlobal existencen
dc.subjectAsymptotic behavioren
dc.subjectFinite time blow-upen
dc.titleGlobal Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactionsen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-185760en
sync.item.dbtypeVAVen
sync.item.insts2025.05.30 12:56:11en
sync.item.modts2025.05.30 12:33:19en
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematikycs
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