Please use this identifier to cite or link to this item:
https://hdl.handle.net/1959.11/7468
Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Du, Yihong | en |
dc.contributor.author | Matano, Hiroshi | en |
dc.date.accessioned | 2011-05-18T16:06:00Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | Journal of the European Mathematical Society, 12(2), p. 279-312 | en |
dc.identifier.issn | 1435-9863 | en |
dc.identifier.issn | 1435-9855 | en |
dc.identifier.uri | https://hdl.handle.net/1959.11/7468 | - |
dc.description.abstract | We study the Cauchy problem ut = uxx + f(u) (t > 0, x ∈ ℝ¹), u(0, x) = uₒ(x) (x ∈ ℝ¹), where f(u) is a locally Lipschitz continuous function satisfying f(0) = 0. We show that any nonnegative bounded solution with compactly supported initial data converges to a stationary solution as t → ∞. Moreover, the limit is either a constant or a symmetrically decreasing stationary solution. We also consider the special case where f is a bistable nonlinearity and the case where f is a combustion type nonlinearity. Examining the behavior of a parameter-dependent solution uλ, we show the existence of a sharp threshold between extinction (i.e., convergence to 0) and propagation (i.e., convergence to 1). The result holds even if f has a jumping discontinuity at u = 1. | 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 | Convergence and sharp thresholds for propagation in nonlinear diffusion problems | en |
dc.type | Journal Article | en |
dc.identifier.doi | 10.4171/JEMS/198 | en |
dc.subject.keywords | Partial Differential Equations | en |
local.contributor.firstname | Yihong | en |
local.contributor.firstname | Hiroshi | 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.school | Maths | 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-20110309-13565 | en |
local.publisher.place | Switzerland | en |
local.format.startpage | 279 | en |
local.format.endpage | 312 | en |
local.identifier.scopusid | 77954913485 | en |
local.peerreviewed | Yes | en |
local.identifier.volume | 12 | en |
local.identifier.issue | 2 | en |
local.contributor.lastname | Du | en |
local.contributor.lastname | Matano | 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:7636 | en |
dc.identifier.academiclevel | Academic | en |
local.title.maintitle | Convergence and sharp thresholds for propagation in nonlinear diffusion problems | en |
local.output.categorydescription | C1 Refereed Article in a Scholarly Journal | en |
local.search.author | Du, Yihong | en |
local.search.author | Matano, Hiroshi | en |
local.uneassociation | Unknown | en |
local.year.published | 2010 | en |
Appears in Collections: | Journal Article School of Science and Technology |
Files in This Item:
File | Description | Size | Format |
---|
SCOPUSTM
Citations
110
checked on Jan 13, 2024
Page view(s)
1,108
checked on Jan 21, 2024
Items in Research UNE are protected by copyright, with all rights reserved, unless otherwise indicated.