DC Field | Value | Language |
---|---|---|
dc.contributor.author | Jin, Hai-Yang | ko |
dc.contributor.author | Kim, Yong-Jung | ko |
dc.contributor.author | Wang, Zhi-An | ko |
dc.date.accessioned | 2018-07-24T02:57:38Z | - |
dc.date.available | 2018-07-24T02:57:38Z | - |
dc.date.created | 2018-07-16 | - |
dc.date.created | 2018-07-16 | - |
dc.date.created | 2018-07-16 | - |
dc.date.created | 2018-07-16 | - |
dc.date.issued | 2018-07 | - |
dc.identifier.citation | SIAM JOURNAL ON APPLIED MATHEMATICS, v.78, no.3, pp.1632 - 1657 | - |
dc.identifier.issn | 0036-1399 | - |
dc.identifier.uri | http://hdl.handle.net/10203/244536 | - |
dc.description.abstract | We are concerned with the following density-suppressed motility model: u(t) = Delta(gamma(v)u) + mu u(1 - u); v(t) = Delta v + u - v, in a bounded smooth domain Omega subset of R-2 with homogeneous Neumann boundary conditions, where the motility function gamma(v) is an element of C-3([0, infinity)), gamma(v) > 0, gamma'(v) < 0 for all v >= 0, lim(v ->infinity) gamma(v) = 0, and lim(v ->infinity) gamma'(v)/gamma(v) exists. The model is proposed to advocate a new possible mechanism: density-suppressed motility can induce spatio-temporal pattern formation through self-trapping. The major technical difficulty in the analysis of above density-suppressed motility model is the possible degeneracy of diffusion from the condition lim(v ->infinity) gamma(v) = 0. In this paper, by treating the motility function gamma(v) as a weight function and employing the method of weighted energy estimates, we derive the a priori L-infinity-bound of v to rule out the degeneracy and establish the global existence of classical solutions of the above problem with a uniform-in-time bound. Furthermore, we show if it mu > K-0/16 with K-0 = max(0 <= v <=infinity) vertical bar gamma'(v)vertical bar(2)/gamma(v), the constant steady state (1,1) is globally asymptotically stable and, hence, pattern formation does not exist. For small mu > 0, we perform numerical simulations to illustrate aggregation patterns and wave propagation formed by the model. | - |
dc.language | English | - |
dc.publisher | SIAM PUBLICATIONS | - |
dc.title | BOUNDEDNESS, STABILIZATION, AND PATTERN FORMATION DRIVEN BY DENSITY-SUPPRESSED MOTILITY | - |
dc.type | Article | - |
dc.identifier.wosid | 000437010200016 | - |
dc.identifier.scopusid | 2-s2.0-85046364265 | - |
dc.type.rims | ART | - |
dc.citation.volume | 78 | - |
dc.citation.issue | 3 | - |
dc.citation.beginningpage | 1632 | - |
dc.citation.endingpage | 1657 | - |
dc.citation.publicationname | SIAM JOURNAL ON APPLIED MATHEMATICS | - |
dc.identifier.doi | 10.1137/17M1144647 | - |
dc.contributor.localauthor | Kim, Yong-Jung | - |
dc.contributor.nonIdAuthor | Jin, Hai-Yang | - |
dc.contributor.nonIdAuthor | Wang, Zhi-An | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | density-suppressed motility | - |
dc.subject.keywordAuthor | degeneracy | - |
dc.subject.keywordAuthor | large time behavior | - |
dc.subject.keywordAuthor | pattern formation | - |
dc.subject.keywordPlus | PARABOLIC CHEMOTAXIS SYSTEM | - |
dc.subject.keywordPlus | LOGISTIC SOURCE | - |
dc.subject.keywordPlus | BLOW-UP | - |
dc.subject.keywordPlus | GLOBAL EXISTENCE | - |
dc.subject.keywordPlus | MODEL | - |
dc.subject.keywordPlus | DIFFUSION | - |
dc.subject.keywordPlus | GROWTH | - |
dc.subject.keywordPlus | STABILITY | - |
dc.subject.keywordPlus | AGGREGATION | - |
dc.subject.keywordPlus | POPULATION | - |
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