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- Svanstedt, Nils, 1958, et al.
(författare)
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Homogenization of a Wilson-Cowan model for neural fields
- 2013
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Ingår i: Nonlinear Analysis. - : Elsevier BV. - 1468-1218. ; 14:3, s. 1705-1715
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Tidskriftsartikel (refereegranskat)abstract
- Homogenization of Wilson-Cowan type of nonlocal neural field models is investigated. Motivated by the presence of a convolution term in this type of models, we first prove some general convergence results related to convolution sequences. We then apply these results to the homogenization problem of the Wilson-Cowan-type model in a general deterministic setting. Key ingredients in this study are the notion of algebras with mean value and the related concept of sigma-convergence.
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29. |
- Svanstedt, Nils, 1958, et al.
(författare)
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Periodic homogenization of strongly nonlinear reaction-diffusion equations with large reaction terms
- 2013
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Ingår i: Applicable Analysis. - : Informa UK Limited. - 0003-6811 .- 1563-504X. ; 92:7, s. 1357-1378
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Tidskriftsartikel (refereegranskat)abstract
- We study in this article the periodic homogenization problem related to a strongly nonlinear reaction-diffusion equation. Owing to the large reaction term, the homogenized equation has a rather quite different form which puts together both the reaction and convection effects. We show in a special case that the homogenized equation is exactly of a convection-diffusion type. This study relies on a suitable version of the well-known two-scale convergence method.
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