Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions : dedicated to Michel Frémond on the occasion of his seventieth birthday

Abstract

We show that many couplings between parabolic systems for processes in solids can be formulated as a gradient system with respect to the total free energy or the total entropy. This includes Allen-Cahn, Cahn-Hilliard, and reaction-diffusion systems and the heat equation. For this, we write the coupled system as an Onsager system (X,F,K) defining the evolution $dot U$= - K(U) DF(U). Here F is the driving functional, while the Onsager operator K(U) is symmetric and positive semidefinite. If the inverse G=K-1 exists, the triple (X,F,G) defines a gradient system. Onsager systems are well suited to model bulk-interface interactions by using the dual dissipation potential ?*(U, ?)= ư <? K(U) ?>.