Abstract
For the Allen-Cahn equation with balanced nonlinearity, we show the existence of equilibrium internal layers intersecting the boundary of two dimensional bounded smooth domains. Stability analysis is carried out for the layers and local shape of the boundary is classified according to the stability of the layers. Numerical simulations are exhibited which indicate that bifurcations occur as the domain boundary is perturbed.
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Iibun, T., Sakamoto, K. Internal layers intersecting the boundary of domain in the Allen-Cahn equation. Japan J. Indust. Appl. Math. 18, 697–738 (2001). https://doi.org/10.1007/BF03167411
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DOI: https://doi.org/10.1007/BF03167411