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math.AP2011★ 5 cited
Even Symmetry of Some Entire Solutions to the Allen-Cahn Equation in Two Dimensions
Changfeng Gui
In this paper, we prove even symmetry and monotonicity of certain solutions of Allen-Cahn equation in a half plane. We also show that entire solutions with {\it finite Morse index}…
math.AP2011★ 42 cited
Symmetry of Traveling Wave Solutions to the Allen-Cahn Equation in $\Er^2$
Changfeng Gui
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 eq…