Abstract
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.
Original language | English |
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Pages (from-to) | 481-547 |
Number of pages | 67 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 66 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Apr 2013 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics