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June WSPC Proceedings Trim Size: 9in x 6in NataliniAIMI3

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June 19, 2009 20:8 WSPC - Proceedings Trim Size: 9in x 6in NataliniAIMI3 1 MATHEMATICAL MODELS FOR BIOFILMS ON THE SURFACE OF MONUMENTS F. CLARELLI Istituto per le Applicazioni del Calcolo “M.Picone”, CNR, c/o Dip. di Matematica, Universita di Roma “Tor Vergata” Via della Ricerca Scientifica 1, I-00133, Roma, Italy E-mail: C. DI RUSSO Dipartimento di Matematica, Universita degli Studi Roma Tre, Largo San Leonardo Murialdo 1, I-00146, Roma, Italy E-mail: R. NATALINI Istituto per le Applicazioni del Calcolo “M.Picone”, CNR, c/o Dip. di Matematica, Universita di Roma “Tor Vergata” Via della Ricerca Scientifica 1, I-00133, Roma, Italy E-mail: M. RIBOT Laboratoire “J.A.Dieudonne”, Universite de Nice Sophia Antipolis, Parc Valrose F-06108 Nice Cedex 02, France E-mail: In this article, a system of nonlinear hyperbolic-elliptic partial differential equa- tions is introduced to model the formation of biofilms. First, a short introduc- tion to some basic concepts about biofilms is given.

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June 19, 2009 20:8
WSPC - Proceedings Trim Size: 9in x 6in NataliniAIMI3
MATHEMATICAL MODELS FOR BIOFILMS ON THE SURFACE OF MONUMENTS F. CLARELLI Istituto per le Applicazioni del Calcolo “M.Picone”, CNR, c/oDip.diMatematica,Universita`diRomaTorVergataVia della Ricerca Scientifica 1, I-00133, Roma, Italy E-mail: clarelli@iac.rm.cnr.it C. DI RUSSO DipartimentodiMatematica,Universita`degliStudiRomaTre, Largo San Leonardo Murialdo 1, I-00146, Roma, Italy E-mail: dirusso@mat.uniroma3.it R. NATALINI Istituto per le Applicazioni del Calcolo “M.Picone”, CNR, c/oDip.diMatematica,Universita`diRomaTorVergataVia della Ricerca Scientifica 1, I-00133, Roma, Italy E-mail: r.natalini@iac.cnr.it http://www.iac.rm.cnr.it/ natalini/ M. RIBOT LaboratoireJ.A.Dieudonne´,Universite`deNiceSophiaAntipolis, Parc Valrose F-06108 Nice Cedex 02, France E-mail: ribot@unice.fr http://math.unice.fr/ ribot/
In this article, a system of nonlinear hyperbolic-elliptic partial differential equa-tions is introduced to model the formation of biofilms. First, a short introduc-tion to some basic concepts about biofilms is given. Then a detailed derivation of the model is presented, which is mainly based on the theory of mixtures, also in comparison with previous models. Adapted numerical schemes will be presented and numerical simulations will be discussed. Keywords : Biofilms; Cyanobacteria; Theory of mixtures; Hyperbolic equations.
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