Multidomain mixed pairs of coupled stationary constrained boundary value problems, are formulated variationally in frameworks of reflexive Banach spaces as macro-hybrid systems, and analyzed. Interior synchronizing and interface coupling transmission constraints are modeled in terms of Lagrange multipliers as solutions of dual variational subpotential maximal monotone inclusions. Existence and uniqueness results are established via resolvent fixed-point characterizations of the corresponding primal and dual macro-hybridized problems. Multimedia mixed mechanical subsurface-surface Darcy/Stokes incompressible flow coupled pairs with intrinsic distributed control constraints exemplify the general macro-hybrid mixed systems. Coupling dual-primal and primal-dual interface macro-hybrid mixed variational conditions are lastly developed and applied to the Darcy/Stokes multimedia pair model.

在自反Banach空间的框架中以宏观混合系统的形式，对耦合的平稳约束边值问题的多域混合对进行了变式表示，并进行了分析。内部同步和接口耦合传输约束是根据拉格朗日乘子建模的，作为对偶变分亚势最大单调包含的解。存在性和唯一性结果是通过对相应的原始和对偶宏杂交问题进行分辨的定点表征来确定的。具有固有分布控制约束的多媒体混合机械地下-达西/斯托克斯不可压缩流耦合对是一般的宏观混合混合系统的例证。