SIAM Journal on Mathematical Analysis

dc.creatorCortázar-Sanz, María Del Carmen
dc.creatorElgueta, Manuel
dc.creatorQuirós, Fernando
dc.creatorWolanski, Noemi
dc.date2021-08-23T23:00:08Z
dc.date2022-07-07T14:57:48Z
dc.date2021-08-23T23:00:08Z
dc.date2022-07-07T14:57:48Z
dc.date2016
dc.date.accessioned2023-08-22T00:51:41Z
dc.date.available2023-08-22T00:51:41Z
dc.identifier1150028
dc.identifier1150028
dc.identifierhttps://hdl.handle.net/10533/252768
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/8302846
dc.descriptionWe study the large time behavior of solutions to the nonlocal diffusion equation partial derivative(t)u = J * u - u in an exterior one-dimensional domain, with zero Dirichlet data on the complement. In the far field scale, xi 1 <= vertical bar x vertical bar t(-1/2) <= xi 2, xi 1, xi 2 > 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, vertical bar x vertical bar <= t(1/2)h(t), lim(t ->infinity) h(t) = 0, the solution scaled by a factor t(3/2) /(vertical bar x vertical bar + 1) converges to a stationary solution of the problem that behaves as b(+/-)x as x -> +/-infinity. The constants b(+/-) are obtained through a matching procedure with the far field limit. In the very far field, vertical bar x vertical bar >= t(1/2)g(t), g(t) -> infinity, the solution decays as o(t(-1)). Keywords Author Keywords:nonlocal diffusion
dc.descriptionexterior domain
dc.descriptionasymptotic behavior
dc.descriptionmatched asymptotics
dc.descriptionRegular 2015
dc.descriptionFONDECYT
dc.descriptionFONDECYT
dc.languageeng
dc.relationhandle/10533/111557
dc.relationhandle/10533/111541
dc.relationhandle/10533/108045
dc.relationhttps://dialnet.unirioja.es/descarga/articulo/6577821.pdf
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 Chile
dc.rightshttp://creativecommons.org/licenses/by-nc-nd/3.0/cl/
dc.rightsinfo:eu-repo/semantics/article
dc.rightsinfo:eu-repo/semantics/openAccess
dc.titleAsymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
dc.titleSIAM Journal on Mathematical Analysis
dc.typeArticulo
dc.typeinfo:eu-repo/semantics/publishedVersion


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