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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Kuto, K., & Tsujikawa, T. (2013). Bifurcation structure of steady-states for bistable equations with nonlocal constraint. Discrete and Continuous Dynamical Systems - Series S, (SUPPL.), 467-476.