We construct new examples of traveling wave solutions to the bistable and balanced semilinear parabolic equation in. Our first example is that of a traveling wave solution with two non planar fronts that move with the same speed. Our second example is a traveling wave solution with a nonconvex moving front. To our knowledge no existence results of traveling fronts with these type of geometric characteristics have been previously known. Our approach explores a connection between solutions of the semilinear parabolic PDE and eternal solutions to the mean curvature flow in.
ASJC Scopus subject areas
- Applied Mathematics