an Entity references as follows:
The Allen–Cahn equation (after John W. Cahn and Sam Allen) 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 .