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https://hdl.handle.net/1959.11/18233
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DC Field | Value | Language |
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dc.contributor.author | Cai, Jingjing | en |
dc.contributor.author | Lou, Bendong | en |
dc.contributor.author | Zhou, Maolin | en |
dc.date.accessioned | 2015-12-08T10:17:00Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | Journal of Dynamics and Differential Equations, 26(4), p. 1007-1028 | en |
dc.identifier.issn | 1572-9222 | en |
dc.identifier.issn | 1040-7294 | en |
dc.identifier.uri | https://hdl.handle.net/1959.11/18233 | - |
dc.description.abstract | We study a nonlinear diffusion equation of the form ut = uxx + f (u) (x ε [g(t), h(t)]) with free boundary conditions g'(t) = -ux(t, g(t)) + α and h'(t) = -ux(t, h(t)) - α for some α > 0. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundaries representing the expanding fronts. When α = 0, the problem was recently investigated by Du and Lin (SIAM J Math Anal 42:377-405, 2010) and Du and Lou (J Euro Math Soc arXiv:1301.5373). In this paper we consider the case α > 0. In this case shrinking (i.e. h(t)-g(t) → 0) may happen, which is quite different from the case α = 0. Moreover, we show that, under certain conditions on f, shrinking is equivalent to vanishing (i.e. u → 0), both of them happen as t tends to some finite time. On the other hand, every bounded and positive time-global solution converges to a nonzero stationary solution as t → ∞. As applications, we consider monostable, bistable and combustion types of nonlinearities, and obtain a complete description on the asymptotic behavior of the solutions. | en |
dc.language | en | en |
dc.publisher | Springer New York LLC | en |
dc.relation.ispartof | Journal of Dynamics and Differential Equations | en |
dc.title | Asymptotic Behavior of Solutions of a Reaction Diffusion Equation with Free Boundary Conditions | en |
dc.type | Journal Article | en |
dc.identifier.doi | 10.1007/s10884-014-9404-z | en |
dcterms.accessRights | Green | en |
dc.subject.keywords | Partial Differential Equations | en |
local.contributor.firstname | Jingjing | en |
local.contributor.firstname | Bendong | en |
local.contributor.firstname | Maolin | 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 | mzhou6@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-20151208-08374 | en |
local.publisher.place | United States of America | en |
local.format.startpage | 1007 | en |
local.format.endpage | 1028 | en |
local.url.open | https://arxiv.org/abs/1406.4629 | en |
local.peerreviewed | Yes | en |
local.identifier.volume | 26 | en |
local.identifier.issue | 4 | en |
local.access.fulltext | Yes | en |
local.contributor.lastname | Cai | en |
local.contributor.lastname | Lou | en |
local.contributor.lastname | Zhou | en |
dc.identifier.staff | une-id:mzhou6 | en |
local.profile.role | author | en |
local.profile.role | author | en |
local.profile.role | author | en |
local.identifier.unepublicationid | une:18438 | en |
dc.identifier.academiclevel | Academic | en |
local.title.maintitle | Asymptotic Behavior of Solutions of a Reaction Diffusion Equation with Free Boundary Conditions | en |
local.output.categorydescription | C1 Refereed Article in a Scholarly Journal | en |
local.search.author | Cai, Jingjing | en |
local.search.author | Lou, Bendong | en |
local.search.author | Zhou, Maolin | en |
local.uneassociation | Unknown | en |
local.year.published | 2014 | en |
local.subject.for2020 | 490410 Partial differential equations | en |
local.subject.seo2020 | 280118 Expanding knowledge in the mathematical sciences | en |
Appears in Collections: | Journal Article |
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