Abstract
This paper studies traveling front solutions of convex polyhedral shapes in bistable reaction-diffusion equations including the Allen-Cahn equations or the Nagumo equations. By taking the limits of such solutions as the lateral faces go to in finity, we construct a three-dimensional traveling front solution for any given g ε C ∞(S 1) with min0≤θ2≤ π g(θ) = 0.
| Original language | English |
|---|---|
| Pages (from-to) | 1011-1046 |
| Number of pages | 36 |
| Journal | Discrete and Continuous Dynamical Systems |
| Volume | 32 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Mar 2012 |
| Externally published | Yes |
Keywords
- Allen-Cahn equation
- Multi-dimensional wave.
- Traveling wave
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics