Singular Limit Problem of Reaction-Diffusion System of Activator-Inhibitor Type

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  • 活性因子・抑制因子型反応拡散系の特異極限問題とパターン形成
  • カッセイ インシ ヨクセイ インシガタ ハンノウ カクサンケイ ノ トクイ キョクゲン モンダイ ト パターン ケイセイ

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Abstract

Reaction-diffusion system of activator-inhibitor type is studied. We considered the functionals containing a small parameter and a long-range interaction. Such functionals arise from the stationary problem of reaction-diffusion system and from the model for phase separation in diblock copolymers. In one dimensional case, we identify global minimizers on an interval of arbitrary length. In two dimensional case, we show that hexagonal structure has the least energy among all periodic dot patterns. Also we show the existence of non-radial solutions.

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