| Abstract: |
| For a balanced bistable reaction-diffusion equation,
an axisymmetric traveling front has been well studied.
We prove that an axially asymmetric traveling front with
any positive speed does exist in a balanced bistable reaction-diffusion
equation. Our method is as follows. We use a pyramidal traveling front
for an imbalanced reaction-diffusion equation whose cross section
has a major axis and a minor axis.
Preserving the major axis and the minor axis
to be given constants and taking the balanced limit,
we obtain an axially asymmetric traveling front in a balanced bistable
reaction-diffusion equation.
This traveling front is monotone decreasing with respect
to the traveling axis, and its cross section is a compact set with
a major axis and a minor axis. |
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