Symmetry of Traveling Wave Solutions to the Allen-Cahn Equation in $\Er^2$
arXiv:1102.4020 · doi:10.1007/s00205-011-0480-5
Abstract
In this paper, we prove even symmetry of monotone traveling wave solutions to the balanced Allen-Cahn equation in the entire plane. Related results for the unbalanced Allen-Cahn equation are also discussed.
References in corpus (1)
Cited by in corpus (5)
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- Modica type gradient estimates for reaction-diffusion equations and a parabolic counterpart of a conjecture of De Giorgi
- Ancient shrinking spherical interfaces in the Allen-Cahn flow
- Traveling wave solutions for bistable fractional Allen-Cahn equations with a pyramidal front