偏微分方程式セミナー(2016/4/8): Reaction-diffusion approximation for understanding pattern formations through non-local interactions, 田中 吉太郎 氏 (北海道大学)

開催日時
2016年   4月 8日 16時 30分 ~ 2016年   4月 8日 17時 30分
場所
北海道大学理学部3号館3-309室
講演者
田中 吉太郎 氏 (北海道大学)
 
Recently, various non-local interactions have been observed, for example, in the neural firing phenomena, non-local dispersal and pigment cells in fish skin. To investigate the mechanisms the non-local evolution equations characterized by the convolution with the suitable kernels were proposed.

In this talk, to specify the relationship between the destabilization of the stable homogeneous state by the non-local interaction and the shape of the kernel in the convolution, a non-local evolution equation is analyzed in one dimension. It is shown that the non-local evolution equation can be approximated by a reaction-diffusion system through the singular limit analysis. It clarifies that the non-local interaction induces the diffusion driven instability and specifies the relationship between the destabilization of the solution and the kernel shape. Finally, it is shown that, for any even convolution kernel, there is a reaction-diffusion system which approximates it.

関連項目

研究集会・セミナー・集中講義の一覧へ