Asymptotic and numerical analysis of the Allen-Cahn equation with a mass constraint
The Allen-Cahn equation with a mass constraint is analyzed asymptotically and numerically in a two-dimensional domain. This problem models the phase separation of a binary mixture in the presence of a mass constraint. Solutions develop internal layers, or interfaces, that propagate depending on t...
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| Language: | English |
| Published: |
2009
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| Online Access: | http://hdl.handle.net/2429/6432 |
| Summary: | The Allen-Cahn equation with a mass constraint is analyzed asymptotically and numerically
in a two-dimensional domain. This problem models the phase separation of a binary mixture
in the presence of a mass constraint. Solutions develop internal layers, or interfaces, that
propagate depending on the curvature of the interfaces while keeping the area they enclose
constant. Small interfaces attached to the boundary of the domain are shown to move along
the boundary in the direction of increasing boundary curvature. The motion of the interfaces
is simulated numerically to verify these asymptotic results. The slow motion behavior of a
semi-circular interface intersecting aflat boundary segment is also analyzed. The projection
method is used to derive an explicit ordinary differential equation for the location of the center
of such a semi-circular interface. |
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