Bifurcation structure of steady-states for bistable equations with nonlocal constraint

Kousuke Kuto, Tohru Tsujikawa

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper studies the 1D Neumann problem of bistable equations with nonlocal constraint. We obtain the global bifurcation structure of solutions by a level set analysis for the associate integral mapping. This structure implies that solutions can form a saddle-node bifurcation curve connecting boundary-layer states with internal-layer states. Furthermore, we exhibit the applications of our result to a couple of shadow systems arising in surface chemistry and physiology.

Original languageEnglish
Pages (from-to)467-476
Number of pages10
JournalDiscrete and Continuous Dynamical Systems - Series S
Issue numberSUPPL.
Publication statusPublished - 2013 Jan 1
Externally publishedYes

Fingerprint

Bifurcation
Internal Layers
Bifurcation Curve
Saddle-node Bifurcation
Global Bifurcation
Physiology
Neumann Problem
Surface chemistry
Level Set
Chemistry
Boundary Layer
Boundary layers
Imply

Keywords

  • Allen-Cahn equation
  • Level set
  • Nonlocal constraint
  • Saddle-node bifurcation
  • Shadow system

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

Bifurcation structure of steady-states for bistable equations with nonlocal constraint. / Kuto, Kousuke; Tsujikawa, Tohru.

In: Discrete and Continuous Dynamical Systems - Series S, No. SUPPL., 01.01.2013, p. 467-476.

Research output: Contribution to journalArticle

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