On variational modeling of Phase-Field-Reaction dynamics
Please login to view abstract download link
We develop a variational framework in which phase‑field evolution and reaction–diffusion dynamics arise from the same underlying order parameter and are jointly determined by multiple contributions to the free energy and dissipation. Starting from a unified energetic formulation, we derive a Cahn–Hilliard‑type system augmented by nonlinear reaction terms that reflect chemical or biological transformations of the phases themselves. The coupling is encoded directly through the structure of the energy and dissipation functionals, allowing interfacial forces, mixing energetics, and reaction kinetics to interact within a single variationally derived system. This approach extends classical phase‑field models by incorporating nonlinear reaction mechanisms while preserving an overall energy dissipation principle. The resulting framework provides a flexible tool for studying interface evolution driven by both diffusive transport and intrinsic phase transformations, with preliminary computations illustrating how these coupled effects shape morphology dynamics.
