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https://hdl.handle.net/1959.11/18389
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DC Field | Value | Language |
---|---|---|
dc.contributor.author | Du, Yihong | en |
dc.contributor.author | Lou, Bendong | en |
dc.date.accessioned | 2016-01-11T15:18:00Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Journal of the European Mathematical Society, 17(10), p. 2673-2724 | en |
dc.identifier.issn | 1435-9863 | en |
dc.identifier.issn | 1435-9855 | en |
dc.identifier.uri | https://hdl.handle.net/1959.11/18389 | - |
dc.description.abstract | We study nonlinear diffusion problems of the form ut = uxx + f (u) with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For special f (u) of the Fisher-KPP type, the problem was investigated by Du and Lin [DL]. Here we consider much more general nonlinear terms. For any f (u) which is Ϲ¹ and satisfies f (0) = 0, we show that the omega limit set ω(u) of every bounded positive solution is determined by a stationary solution. For monostable, bistable and combustion types of nonlinearities, we obtain a rather complete description of the long-time dynamical behavior of the problem; moreover, by introducing a parameter σ in the initial data, we reveal a threshold value σ* such that spreading (limt→∞u = 1) happens when σ > σ*, vanishing (limt→∞u = 0) happens when σ < σ*, and at the threshold value σ*, ω(u) is different for the three different types of nonlinearities. When spreading happens, we make use of "semi-waves" to determine the asymptotic spreading speed of the front. | en |
dc.language | en | en |
dc.publisher | European Mathematical Society Publishing House | en |
dc.relation.ispartof | Journal of the European Mathematical Society | en |
dc.title | Spreading and vanishing in nonlinear diffusion problems with free boundaries | en |
dc.type | Journal Article | en |
dc.identifier.doi | 10.4171/JEMS/568 | en |
dcterms.accessRights | Green | en |
dc.subject.keywords | Partial Differential Equations | en |
local.contributor.firstname | Yihong | en |
local.contributor.firstname | Bendong | en |
local.subject.for2008 | 010110 Partial Differential Equations | en |
local.subject.seo2008 | 970101 Expanding Knowledge in the Mathematical Sciences | en |
local.profile.school | School of Science and Technology | en |
local.profile.email | ydu@une.edu.au | en |
local.output.category | C1 | en |
local.record.place | au | en |
local.record.institution | University of New England | en |
local.identifier.epublicationsrecord | une-20151223-17085 | en |
local.publisher.place | Switzerland | en |
local.format.startpage | 2673 | en |
local.format.endpage | 2724 | en |
local.identifier.scopusid | 84934451605 | en |
local.url.open | https://arxiv.org/abs/1301.5373 | en |
local.peerreviewed | Yes | en |
local.identifier.volume | 17 | en |
local.identifier.issue | 10 | en |
local.access.fulltext | Yes | en |
local.contributor.lastname | Du | en |
local.contributor.lastname | Lou | en |
dc.identifier.staff | une-id:ydu | en |
local.profile.orcid | 0000-0002-1235-0636 | en |
local.profile.role | author | en |
local.profile.role | author | en |
local.identifier.unepublicationid | une:18592 | en |
dc.identifier.academiclevel | Academic | en |
local.title.maintitle | Spreading and vanishing in nonlinear diffusion problems with free boundaries | en |
local.output.categorydescription | C1 Refereed Article in a Scholarly Journal | en |
local.relation.grantdescription | ARC/DP120100727 | en |
local.search.author | Du, Yihong | en |
local.search.author | Lou, Bendong | en |
local.uneassociation | Unknown | en |
local.year.published | 2015 | en |
local.subject.for2020 | 490410 Partial differential equations | en |
local.subject.seo2020 | 280118 Expanding knowledge in the mathematical sciences | en |
local.codeupdate.date | 2021-11-08T15:57:40.990 | en |
local.codeupdate.eperson | ydu@une.edu.au | en |
local.codeupdate.finalised | true | en |
local.original.for2020 | 490410 Partial differential equations | en |
local.original.seo2020 | 280118 Expanding knowledge in the mathematical sciences | en |
Appears in Collections: | Journal Article School of Science and Technology |
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