Allen-Cahn equation with matrix-valued anisotropic mobility in two-dimensional space

초록

The Allen-Cahn equation models antiphase domain coarsening in binary mixtures. To capture more complex and natural dynamics, we derive the anisotropic Allen-Cahn (aAC) equation, incorporating anisotropic mobility from an energy functional with a matrix-valued mobility. We present properties of the aAC equation, including energy dissipation and linear stability analysis, using this energy functional. The semi-discretized aAC equation is studied for properties like unique solvability, the maximum principle, and unconditional energy-gradient stability in a time-discrete manner. Additionally, numerical experiments demonstrate properties such as the maximum principle, unconditional energy stability, linear stability analysis, total area decreasing property, and transition layer profile.

키워드