Allen–Cahn equation
The Allen–Cahn equation is a reaction–diffusion equation of mathematical physics which describes the process of phase separation in multi-component alloy systems, including order-disorder transitions.
The equation describes the time evolution of a scalar-valued state variable on a domain during a time interval,
and is given by:
where is the mobility, is a double-well potential, is the control on the state variable at the portion of the boundary, is the source control at, is the initial condition,
and is the outward normal to .
It is the L2 gradient flow of the Ginzburg–Landau free energy functional. It is closely related to the Cahn–Hilliard equation.
