| Abstract: |
| We study polyhedral entire solutions to a bistable reaction-diffusion equation
in $\mathbb{R}^{n}$.
We consider a pyramidal traveling front solution
to the same equation in $\mathbb{R}^{n+1}$.
As the speed goes to infinity,
its projection converges to an $n$-dimensional polyhedral entire solution.
Conversely, as the time goes to $-\infty$, an
$n$-dimensional polyhedral entire solution
gives $n$-dimensional pyramidal traveling front solutions.
The result in this paper suggests a correlation between
traveling front solutions and entire solutions
in general reaction-diffusion equations or systems. |
|