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dc.contributor.author
Cortázar, Carmen
dc.contributor.author
Elgueta, Manuel
dc.contributor.author
Quirós, Fernando
dc.contributor.author
Wolanski, Noemi Irene
dc.date.available
2017-06-26T20:42:54Z
dc.date.issued
2016-03
dc.identifier.citation
Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi Irene; Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains; Siam Publications; Siam Journal On Mathematical Analysis; 48; 3; 3-2016; 1549-1574
dc.identifier.issn
0036-1410
dc.identifier.uri
http://hdl.handle.net/11336/18936
dc.description.abstract
We study the long time behavior of solutions to the nonlocal diffusion equation ∂tu = J ∗ u − u in an exterior one-dimensional domain, with zero Dirichlet data on the complement. In the far field scale, ξ1 ≤ |x|t −1/2 ≤ ξ2, ξ1, ξ2 > 0, this behavior is given by a multiple of the dipole solution for the local heat equation with a diffusivity determined by J. However, the proportionality constant is not the same on R+ and R−: it is given by the asymptotic first moment of the solution on the corresponding half line, which can be computed in terms of the initial data. In the near field scale, |x| ≤ t 1/2h(t), limt→∞ h(t) = 0, the solution scaled by a factor t 3/2 /(|x| + 1) converges to a stationary solution of the problem that behaves as b ±x as x → ±∞. The constants b ± are obtained through a matching procedure with the far field limit. In the very far field, |x|≥t 1/2 g(t), g(t) → ∞, the solution has order o(t −1 ).
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Siam Publications
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Difusión No Local
dc.subject
Comportamiento Asintótico
dc.subject.classification
Matemática Pura
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2017-06-26T14:08:58Z
dc.identifier.eissn
1095-7154
dc.journal.volume
48
dc.journal.number
3
dc.journal.pagination
1549-1574
dc.journal.pais
Estados Unidos
dc.description.fil
Fil: Cortázar, Carmen. Pontificia Universidad Católica de Chile; Chile
dc.description.fil
Fil: Elgueta, Manuel. Pontificia Universidad Católica de Chile; Chile
dc.description.fil
Fil: Quirós, Fernando. Universidad Autónoma de Madrid; España
dc.description.fil
Fil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
dc.journal.title
Siam Journal On Mathematical Analysis
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1137/151006287
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://epubs.siam.org/doi/abs/10.1137/151006287
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1412.0731
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