Proves global existence of weak solutions and conditional 2D uniqueness for a Brinkman-biofilm-nutrient PDE system with volume-fraction constraints via fixed-point and compactness arguments.
Ulbrich.Semismooth Newton methods for variational inequalities and constrained optimization problems in function spaces, SIAM, Philadelphia, PA, 2011
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Well-Posedness of a Coupled Brinkman--Biofilm--Nutrient System with Volume-Fraction Constraints
Proves global existence of weak solutions and conditional 2D uniqueness for a Brinkman-biofilm-nutrient PDE system with volume-fraction constraints via fixed-point and compactness arguments.