| Abstract: |
| Let $n\geq 2$ be a given integer.
In this paper, we assert that
an $n$-dimensional traveling front converges to
an $(n-1)$-dimensional entire solution
as the speed goes to infinity
in a balanced bistable reaction-diffusion equation.
As the speed of an $n$-dimensional axially symmetric or asymmetric
traveling front goes to infinity,
it converges to an $(n-1)$-dimensional radially symmetric or asymm\
etric
entire solution
in a balanced bistable reaction-diffusion equation, respectively.
We conjecture that
the radially asymmetric entire solutions obtained
in this paper are associated with the ancient solutions called
the Angenent ovals in the mean curvature flows. |
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