Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
study the large time behavior of solutions to the nonlocal diffusion equation ℓtu = J-u-u in an exterior one-dimensional domain, with zero Dirichlet data on the complement. In the far field scale, ζ1 ≤ |x|t.1/2 ≤ ζ2, ζ1, ζ2 > 0, this behavior is given by a multiple of the dipole solution for...
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2016
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v48_n3_p1549_Cortazar http://hdl.handle.net/20.500.12110/paper_00361410_v48_n3_p1549_Cortazar |
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| Sumario: | study the large time behavior of solutions to the nonlocal diffusion equation ℓtu = J-u-u in an exterior one-dimensional domain, with zero Dirichlet data on the complement. In the far field scale, ζ1 ≤ |x|t.1/2 ≤ ζ2, ζ1, ζ2 > 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| ≤ t1/2h(t), limt→h(t) = 0, the solution scaled by a factor t3/2/(|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|≤t1/2g(t), g(t)→, the solution decays as o(t-1). © by SIAM. |
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