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Traveling Waves with Multiple and Nonconvex Fronts for a Bistable Semilinear Parabolic Equation
Author(s) -
del Pino Manuel,
Kowalczyk Michał,
Wei Juncheng
Publication year - 2013
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21438
Subject(s) - mathematics , bistability , traveling wave , curvature , mathematical analysis , front (military) , parabolic partial differential equation , mean curvature flow , connection (principal bundle) , planar , wave equation , flow (mathematics) , geometry , mean curvature , partial differential equation , physics , computer graphics (images) , quantum mechanics , meteorology , computer science
We construct new examples of traveling wave solutions to the bistable and balanced semilinear parabolic equation in \input amssym ${\Bbb R}^N+1$ , $N\geq 2$ . 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 \input amssym ${\Bbb R}^N+1$ .