Control nonlinear diffusion macro‐hybrid mixed variational problems

Monotone control nonlinear diffusion, primal macro‐hybrid mixed variational problems, in reflexive Banach spaces, are analyzed. Composition duality principles, based on coupling compatibility conditions, establish macro‐hybrid, mixed and primal equivalent variational solvabilities. Qualitative properties as existence, uniqueness and stability are determined. Macro‐hybridization is performed for spatial parallel analysis and computation, in terms of non‐overlapping multidomain decompositions, with primal transmission conditions dualized.