Asymptotic behavior for nonlocal diffusion equations
- Chasseigne, Emmanuel
- Chaves, Manuela
- Rossi, Julio D.
DOIAbstract
AbstractWe study the asymptotic behavior for nonlocal diffusion models of the form ut=J∗u−u in the whole RN or in a bounded smooth domain with Dirichlet or Neumann boundary conditions. In RN we obtain that the long time behavior of the solutions is determined by the behavior of the Fourier transform of J near the origin, which is linked to the behavior of J at infinity. If Jˆ(ξ)=1−A|ξ|α+o(|ξ|α) (0<α⩽2), the asymptotic behavior is the same as the one for solutions of the evolution given by the α/2 fractional power of the Laplacian. In particular when the nonlocal diffusion is given by a compactly supported kernel the asymptotic behavior is the same as the one for the heat equation, which is yet a local model. Concerning the Dirichlet problem...
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