Multi-component conserved Allen–Cahn equations
M Grasselli, A Poiatti�- Interfaces and Free Boundaries, 2024 - ems.press
We consider a multi-component version of the conserved Allen–Cahn equation proposed by
J. Rubinstein and P. Sternberg in 1992 as an alternative model for phase separation. In our
case, the free energy is characterized by a mixing entropy density which belongs to a large
class of physically relevant entropies like, for example, the Boltzmann–Gibbs entropy. We
establish the well-posedness of the Cauchy–Neumann problem with respect to a natural
notion of (finite) energy solution which is more regular under appropriate assumptions and is�…
J. Rubinstein and P. Sternberg in 1992 as an alternative model for phase separation. In our
case, the free energy is characterized by a mixing entropy density which belongs to a large
class of physically relevant entropies like, for example, the Boltzmann–Gibbs entropy. We
establish the well-posedness of the Cauchy–Neumann problem with respect to a natural
notion of (finite) energy solution which is more regular under appropriate assumptions and is�…