Carpio Rodríguez, Ana MaríaDuro, Gema2024-10-172024-10-1720240362-546X10.1016/j.na.2024.113538https://hdl.handle.net/20.500.14352/1090422024 acuerdo transformativo CRUEWe consider a quasi-stationary problem describing the status of velocities, pressures and chemicals affecting cell behavior within a biofilm. The model couples stationary transport equations and compressible Stokes systems with convection–reaction–diffusion equations. We establish existence, uniqueness and stability of solutions of the different submodels involved and then obtain well posedness results for the quasi-stationary system. Our analysis relies on the construction of weak solutions for the steady transport equations under sign assumptions and the reformulation of the compressible Stokes problem as an elliptic system with enhanced regularity properties on the pressure. We need to consider velocity fields whose divergence and normal boundary components satisfy sign conditions. Applications include the study of cells, biofilms and tissues, where one phase is a liquid solution, whereas the other one is assorted biomass.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articleopen accessTwo phase flowMixture modelsThin film approximationsStationary transport equationsCompressible Stokes equationsElliptic systemsAnálisis matemáticoEcuaciones diferenciales12 Matemáticas1206.13 Ecuaciones Diferenciales en Derivadas Parciales