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

Kousuke Kuto; Tohru Tsujikawa

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

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	467-476
Number of pages	10
Journal	Discrete and Continuous Dynamical Systems - Series S
Issue number	SUPPL.
Publication status	Published - 2013 Nov
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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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.",

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AB - 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.

KW - Allen-Cahn equation

KW - Level set

KW - Nonlocal constraint

KW - Saddle-node bifurcation

KW - Shadow system

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