| Abstract: |
| Traveling waves appear in various phenomena and
there are a lot of results related to traveling waves in PDEs describing such phenomena.
Here we pay attention to traveling wave solutions
for mean curvature flow with a driving force.
As is well known, Grim reaper and V-shaped traveling front are typical examples
of traveling wave solutions for mean curvature flow and eikonal-curvature flow, respectively.
However there are defined in whole space and not compact.
In recent years, the authors have studied about
the existence and uniqueness of
traveling waves composed of Jordan curve in two-dimensinoal space,
called ``compact traveling wave``, under a general driving force.
In this talk, we consider the same problem in more than three-dimensional space.
In particular, we show the existence and uniqueness of axisymmetric
compact traveling waves, which is symmetric with respect to traveling direction,
for the mean curvature flow equation with driving force.
This is a joint work with Hirokazu Ninomiya. |
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