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 |
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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 journal › Article
}
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 -