### 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 Jan 1 |

Externally published | Yes |

### Fingerprint

### 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

*Discrete and Continuous Dynamical Systems - Series S*, (SUPPL.), 467-476.

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

Research output: Contribution to journal › Article

*Discrete and Continuous Dynamical Systems - Series S*, no. SUPPL., pp. 467-476.

}

TY - JOUR

T1 - Bifurcation structure of steady-states for bistable equations with nonlocal constraint

AU - Kuto, Kousuke

AU - Tsujikawa, Tohru

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84901445990&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84901445990&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84901445990

SP - 467

EP - 476

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

SN - 1937-1632

IS - SUPPL.

ER -