Mixed variational analysis of constrained nonlinear primal and dual evolution problems is performed on the basis of composition duality principles. Existence of evolution solutions of the systems is determined via fixed-point variational analysis results, for regular initial data, as well as, under boundedness and coercivity conditions, for general admissible initial data. As a representative application of the theory, a constrained nonlinear transport-flow model through porous media is treated.

primal and dual mixed variational problems, evolution variational inclusions, composition duality principles, fixed-point variational existence analysis, constrained nonlinear transport-flow in porous media.