The Nonlinear "Hot Spots" Conjecture and Pattern Formation

• Miyamoto Yasuhito

  東京工業大学大学院理工学研究科数学専攻

Bibliographic Information

Other Title

• 非線形ホットスポット予想とパターン形成
• ヒセンケイ ホットスポット ヨソウ ト パターン ケイセイ

Abstract

We will mathematically describe the stable steady states of the shadow system of the activator-inhibitor type in a disk, using the number and the locations of the critical points of the function. Specifically, if the steady state is stable, then the solution has exactly two critical points on the disk and they are on the boundary. Hence the shape of the stable steady state is like a boundary one-spike layer. We will see that our problem can be reduced to the nonlinear "hot spots" conjecture, and that this conjecture is a fundamental theorem in studying the shape of the stable pattern of the shadow system.

Journal

• Bulletin of the Japan Society for Industrial and Applied Mathematics

  Bulletin of the Japan Society for Industrial and Applied Mathematics 19 (1), 16-27, 2009

  The Japan Society for Industrial and Applied Mathematics

Details

• CRID: 1390282680743332352
• NII Article ID: 110007162482
• NII Book ID: AN10288886
• ISSN: 09172270
• ISSN: 24321982
• DOI: 10.11540/bjsiam.19.1_16
• NDL BIB ID: 10241530
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I10241530
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • CiNii Articles
• Abstract License Flag: Disallowed