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DC Field | Value | Language |
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dc.citation.endPage | 297 | - |
dc.citation.startPage | 266 | - |
dc.citation.title | JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | - |
dc.citation.volume | 142 | - |
dc.contributor.author | Choi, Kyudong | - |
dc.contributor.author | Kang, Moon-Jin | - |
dc.contributor.author | Vasseur, Alexis F. | - |
dc.date.accessioned | 2023-12-21T16:50:45Z | - |
dc.date.available | 2023-12-21T16:50:45Z | - |
dc.date.created | 2020-10-07 | - |
dc.date.issued | 2020-10 | - |
dc.description.abstract | We consider a one-dimensional system arising from a chemotaxis model in tumour angiogenesis, which is described by a Keller-Segel equation with singular sensitivity. This hyperbolic-parabolic system is known to allow viscous shocks (so-called traveling waves), and in literature, their nonlinear stability has been considered in the class of certain mean-zero small perturbations. We show the global existence of solution without assuming the mean-zero condition for any initial data as arbitrarily large perturbations around traveling waves in the Sobolev space H-1 while the shock strength is assumed to be small enough. The main novelty of this paper is to develop the global well-posedness of any large H-1-perturbations of traveling waves connecting two different end states. The discrepancy of the end states is linked to the complexity of the corresponding flux, which requires a new type of an energy estimate. To overcome this issue, we use the a priori contraction estimate of a weighted relative entropy functional up to a translation, which was proved by Choi-Kang-Kwon-Vasseur [1]. The boundedness of the shift implies a priori bound of the relative entropy functional without the shift on any time interval of existence, which produces a H-1-estimate thanks to a De Giorgi type lemma. Moreover, to remove possibility of vacuum appearance, we use the lemma again. (C) 2020 Elsevier Masson SAS. All rights reserved. | - |
dc.identifier.bibliographicCitation | JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v.142, pp.266 - 297 | - |
dc.identifier.doi | 10.1016/j.matpur.2020.03.002 | - |
dc.identifier.issn | 0021-7824 | - |
dc.identifier.scopusid | 2-s2.0-85081949347 | - |
dc.identifier.uri | https://scholarworks.unist.ac.kr/handle/201301/48283 | - |
dc.identifier.url | https://www.sciencedirect.com/science/article/pii/S0021782420300568 | - |
dc.identifier.wosid | 000569224900011 | - |
dc.language | 영어 | - |
dc.publisher | ELSEVIER | - |
dc.title | Global well-posedness of large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model | - |
dc.type | Article | - |
dc.description.isOpenAccess | FALSE | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied; Mathematics | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.type.docType | Article | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.subject.keywordAuthor | Tumour angiogenesis | - |
dc.subject.keywordAuthor | Keller-Segel | - |
dc.subject.keywordAuthor | Stability | - |
dc.subject.keywordAuthor | Global existence | - |
dc.subject.keywordAuthor | Traveling wave | - |
dc.subject.keywordAuthor | Conservation laws | - |
dc.subject.keywordPlus | INITIATION | - |
dc.subject.keywordPlus | BACTERIA | - |
dc.subject.keywordPlus | MATHEMATICAL-MODEL | - |
dc.subject.keywordPlus | STABILITY | - |
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