E. Alpkvist and I. Klapper, A Multidimensional Multispecies Continuum Model for Heterogeneous Biofilm Development, Bulletin of Mathematical Biology, vol.69, issue.7, pp.765-789, 2007.
DOI : 10.1007/s11538-007-9212-2

A. D. Preziosi and L. , On the closure of mass balance models for tumor growth, Math. Models Methods Appl. Sci, vol.12, pp.737-754, 2002.

K. Anguige, J. R. King, and J. P. Ward, A multi-phase mathematical model of quorum sensing in a maturing Pseudomonas aeruginosa biofilm, Mathematical Biosciences, vol.203, issue.2, pp.240-276, 2006.
DOI : 10.1016/j.mbs.2006.05.009

D. Aregba-driollet and R. Natalini, Discrete Kinetic Schemes for Multidimensional Systems of Conservation Laws, SIAM Journal on Numerical Analysis, vol.37, issue.6, 1973.
DOI : 10.1137/S0036142998343075
URL : https://hal.archives-ouvertes.fr/hal-00959531

S. Astanin and L. Preziosi, Multiphase models of tumor growth., Selected topics in cancer modeling, Model. Simul. Sci. Eng. Technol, pp.223-253, 2008.

A. Chorin, Numerical solution of the Navier-Stokes equations, Mathematics of Computation, vol.22, issue.104, pp.745-762, 1968.
DOI : 10.1090/S0025-5718-1968-0242392-2

F. Clarelli, D. Russo, C. Natalini, R. Ribot, and M. , Multidimensional model of biofilm growth : stability and influence of environment
URL : https://hal.archives-ouvertes.fr/hal-01070624

R. Congestri, D. Pippo, F. De-philippis, R. Buttino, I. Paradossi et al., Seasonal succession of phototrophic biofilms in an Italian wastewater treatment plant: biovolume, spatial structure and exopolysaccharides, Aquatic Microbial Ecology, vol.45, pp.301-312, 2006.
DOI : 10.3354/ame045301

J. W. Costerton, G. G. Geesey, and K. J. Cheng, How Bacteria Stick, Scientific American, vol.238, issue.1, pp.86-95, 1978.
DOI : 10.1038/scientificamerican0178-86

C. A. Crispim and C. C. Gaylarde, Cyanobacteria and Biodeterioration of Cultural Heritage: A Review, Microbial Ecology, vol.45, issue.1, pp.1-9, 2005.
DOI : 10.1007/s00248-003-1052-5

O. A. Cuzman, S. Ventura, and C. Sili, Biodiversity of phototrophic biofilms dwelling on monumental fountains, Microbial Ecology, pp.81-95, 2010.

D. Pippo, F. Bohn, A. Congestri, R. De-philippis, R. Albertano et al., Capsular polysaccharides of cultured phototrophic biofilms, Biofouling, vol.52, issue.6, pp.495-504, 2009.
DOI : 10.1016/j.mimet.2007.05.013

H. Eberl, E. Morgenroth, D. Noguera, C. Picioreanu, B. Rittmann et al., Mathematical modeling of biofilm, Scientific and, 2006.

P. H. Eilers and J. C. Peeters, A model for the relationship between light intensity and the rate of photosynthesis in phytoplankton, Ecological Modelling, vol.42, issue.3-4, pp.3-4, 1988.
DOI : 10.1016/0304-3800(88)90057-9

A. Farina and L. Preziosi, On Darcy's law for growing porous media, Int. J. Nonlinear Mech, vol.37, pp.485-491, 2001.

L. Hall-stoodley, J. W. Costerton, and P. Stoodley, Bacterial biofilms: from the Natural environment to infectious diseases, Nature Reviews Microbiology, vol.146, issue.2, pp.95-108, 2004.
DOI : 10.1016/S0167-7012(99)00097-4

C. H. Johnson, S. S. Golden, and T. Kondoc, Adaptive significance of circadian programs in cyanobacteria, Trends in Microbiology, vol.6, issue.10, pp.407-410, 1998.
DOI : 10.1016/S0966-842X(98)01356-0

I. Klapper and J. Dockery, Mathematical Description of Microbial Biofilms, to appear, SIAM Review, 2009.

I. B. Kuffner and V. J. Paul, Effects of nitrate, phosphate and iron on the growth of macroalgae and benthic cyanobacteria from Cocos Lagoon, Guam, Marine Ecology Progress Series, vol.222, pp.63-72, 2001.
DOI : 10.3354/meps222063

B. J. Ni, R. J. Zeng, F. Fang, J. Xu, G. Sheng et al., A Novel Approach to Evaluate the Production Kinetics of Extracellular Polymeric Substances (EPS) by Activated Sludge Using Weighted Nonlinear Least-Squares Analysis, Environmental Science & Technology, vol.43, issue.10, 2009.
DOI : 10.1021/es9001289

N. C. Overgaard, Application of variational inequalities to the moving-boundary problem in a fluid model for biofilm growth, Nonlinear Analysis: Theory, Methods & Applications, vol.70, issue.10, pp.3658-3664, 2009.
DOI : 10.1016/j.na.2008.07.021

J. C. Peeters and P. H. Eilers, The relationship between light intensity and photosynthesis???A simple mathematical model, Hydrobiological Bulletin, vol.2, issue.2, pp.134-136, 1978.
DOI : 10.1007/BF02260714

K. R. Rajagopal and L. Tao, Mechanics of mixtures, Series on Advances in Mathematics for Applied Sciences, 1995.
DOI : 10.1142/2197

M. Stomp, J. Huisman, L. J. Stal1, and H. C. Matthijs, Colorful niches of phototrophic microorganisms shaped by vibrations of the water molecule, The ISME Journal, vol.32, pp.271-282, 2007.
DOI : 10.1038/ismej.2007.59

R. Temam, Une m??thode d'approximation de la solution des ??quations de Navier-Stokes, Bulletin de la Société mathématique de France, vol.79, pp.115-152, 1968.
DOI : 10.24033/bsmf.1662

R. Temam, Navier Stokes Equations: Theory and Numerical Analysis, Journal of Applied Mechanics, vol.45, issue.2, 2001.
DOI : 10.1115/1.3424338

J. M. Thebault and S. Rabouille, Comparison between two mathematical formulations of the phytoplankton specific growth rate as a function of light and temperature, in two simulation models (Aster & Yoyo), two simulation models (ASTER & YOYO), pp.145-151, 2003.
DOI : 10.1016/S0304-3800(02)00404-0

E. Van-der-grinten, A. P. Janssen, K. De-mutsert, C. Barranguet, and W. Admiraal, Temperature- and Light-Dependent Performance of the Cyanobacterium Leptolyngbya Foveolarum and the Diatom Nitzschia Perminuta in Mixed Biofilms, Hydrobiologia, vol.24, issue.1, pp.267-278, 2005.
DOI : 10.1007/s10750-005-5324-6

O. Wanner and W. Gujer, Competition in biofilms, Wat. Sci. Tech, vol.17, pp.27-44, 1984.

O. Wanner and W. Gujer, A multispecies biofilm model, Biotechnology and Bioengineering, vol.10, issue.3, pp.314-328, 1986.
DOI : 10.1002/bit.260280304

T. Zhang, N. Cogan, and Q. Wang, Phase-field models for biofilms II. 2-D numerical simulations of biofilmflow interaction, Commun. Comput. Phys, vol.4, pp.72-101, 2008.

B. Zippel, J. Rijstenbil, and T. R. Neu, A flow-lane incubator for studying freshwater and marine phototrophic biofilms, Journal of Microbiological Methods, vol.70, issue.2, pp.336-345, 2007.
DOI : 10.1016/j.mimet.2007.05.013