Carpio Rodríguez, Ana MaríaDuro, Gema2023-07-202023-07-202023-07-03Carpio Rodríguez, A. M. & Duro, G. «Well Posedness of Fluid-Solid Mixture Models for Biofilm Spread». Applied Mathematical Modelling, vol. 124, diciembre de 2023, pp. 64-85. DOI.org (Crossref), https://doi.org/10.1016/j.apm.2023.07.005.0307-904X10.1016/j.apm.2023.07.005https://hdl.handle.net/20.500.14352/87292Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves in response to variations in the mechano-chemical variables. For a model of biofilm spread, we show how to improve its stability properties by characterizing the time derivatives of relevant quasi-stationary magnitudes in terms of additional boundary value problems. We also give conditions for well posedness of time dependent submodels set in moving domains depending on the motion of the boundary. After constructing solutions for transport, diffusion and elliptic submodels for volume fractions, displacements, velocities, pressures and concentrations with the required regularity, we are able to handle the full model of biofilm spread in moving domains assuming we know the dynamics of the boundary. These techniques are general and can be applied in models with a similar structure arising in biological applications.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articlehttps//doi.org/10.1016/j.apm.2023.07.005https://www.sciencedirect.com/science/article/pii/S0307904X23003001embargoed accessopen access519.87Fluid-solid mixture modelsThin film approximationsEvolution equations in moving domainsQuasi-stationary approximationsStationary transport equationsBiomatemáticasInvestigación operativa (Matemáticas)2404 Biomatemáticas1207 Investigación Operativa