On limit systems for some population models with cross-diffusion

Kousuke Kuto*, Yoshio Yamada

*この研究の対応する著者

研究成果: Article査読

12 被引用数 (Scopus)

抄録

This paper deals with the following reaction-diffusion system (SP) σ Δ[(1 + αv)u] + u(a-u-cv) = 0, Δ[(1 + βu)v] + v(b-du-v) = 0, in a bounded domain of R N with homogeneous Neumann boundary conditions or Dirichlet boundary conditions. Our main purpose is to understand the structure of positive solutions of (SP) and know the effects of cross-diffusion coefficients α and β. For this purpose, our strategy is to study limiting behavior of positive solutions when α or β goes to ∞ and derive the corresponding limit systems. We will obtain a priori estimates of u and v independently of β (resp. α) with small α & 0 (resp. β ≥ 0) in case 1 ≤ N ≤ 3 under Neumann boundary conditions, while we will obtain a priori estimates of u and v independently of α and β in case 1 ≤ N ≤ 5 under Dirichlet boundary conditions. These a priori estimates allow us to investigate limiting behavior of positive solutions. When α = 0 and β → ∞, we can derive two limit systems for Neumann conditions and one limit system for Dirichlet conditions. We will also give some results on the structure of positive solutions for such limit systems.

本文言語English
ページ(範囲)2745-2769
ページ数25
ジャーナルDiscrete and Continuous Dynamical Systems - Series B
17
8
DOI
出版ステータスPublished - 2012 11月
外部発表はい

ASJC Scopus subject areas

  • 離散数学と組合せ数学
  • 応用数学

フィンガープリント

「On limit systems for some population models with cross-diffusion」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル