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.
|Number of pages||36|
|Journal||Discrete and Continuous Dynamical Systems|
|Publication status||Published - Mar 2012|
- Allen-Cahn equation
- Multi-dimensional wave.
- Traveling wave
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics