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Variational interior and interface transmission conditions: multidomain mixed Darcy/Stokes control problems

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Abstract

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.

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  1. Instituto de Geofísica, Universidad Nacional Autónoma de México, Ciudad de México, Coyoacán, 04510, México

    Gonzalo Alduncin

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  1. Gonzalo Alduncin
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Correspondence to Gonzalo Alduncin.

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Alduncin, G. Variational interior and interface transmission conditions: multidomain mixed Darcy/Stokes control problems. Optim Eng 23, 797–826 (2022). https://doi.org/10.1007/s11081-021-09606-2

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