A. Marrocco, 2d simulation of chemotactic bacteria aggregation, 2002.
URL : https://hal.archives-ouvertes.fr/inria-00071918

E. F. Keller and L. A. Segel, Model for chemotaxis, Journal of Theoretical Biology, vol.30, issue.2, pp.225-234, 1971.
DOI : 10.1016/0022-5193(71)90050-6

M. D. Betterton and M. P. Brenner, Collapsing bacterial cylinders, Physical Review E, vol.64, issue.6, 2001.
DOI : 10.1103/PhysRevE.64.061904

M. P. Brenner, P. Constantin, L. P. Kadanoff, A. Schenkel, and S. C. Venhataramani, Diffusion, attraction and collapse, Nonlinearity, vol.12, issue.4, pp.1071-1098, 1999.
DOI : 10.1088/0951-7715/12/4/320

M. P. Brenner, L. S. Levitov, and E. O. Budrene, Physical Mechanisms for Chemotactic Pattern Formation by Bacteria, Biophysical Journal, vol.74, issue.4, pp.1677-1693, 1998.
DOI : 10.1016/S0006-3495(98)77880-4

L. Corrias, B. Perthame, and H. Zaag, A model motivated by angiogenesis. C. Rendus Acad

M. A. Herrero and J. J. Velázquez, Chemotactic collapse for the Keller-Segel model, Journal of Mathematical Biology, vol.35, issue.2, pp.177-194, 1996.
DOI : 10.1007/s002850050049

R. Tyson, L. G. Stern, and R. J. Leveque, Fractional step methods applied to a chemotaxis model, Journal of Mathematical Biology, vol.41, issue.5, pp.455-475, 2000.
DOI : 10.1007/s002850000038

A. Marrocco, Numerical simulation of chemotactic bacteria aggregation via mixed finite elements. RAIRO-M 2 AN, pp.617-630, 2003.

A. Blanchet, J. Dolbeault, and B. Perthame, Two-dimensional keller-segel model: Optimal critical mass and qualitative properties of the solutions, Electron. J. Diff. Eqns, issue.44, pp.1-32, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00113519

V. Calvez and B. Perthame, A Lyapunov function for a two-chemical species version of the chemotaxis model, BIT Numerical Mathematics, vol.64, issue.S1, 2006.
DOI : 10.1007/s10543-006-0086-8

B. Perthame, Transport equations in biology, Frontiers in Mathematics, 2006.

M. Mimura, H. Sakaguchi, and M. Matsushita, Reaction???diffusion modelling of bacterial colony patterns, Physica A: Statistical Mechanics and its Applications, vol.282, issue.1-2, pp.283-303, 2000.
DOI : 10.1016/S0378-4371(00)00085-6

I. Golding, Y. Kozlovsky, I. Cohen, and E. Ben-jacob, Studies of bacterial branching growth using reaction???diffusion models for colonial development, Physica A: Statistical Mechanics and its Applications, vol.260, issue.3-4, pp.510-554, 1998.
DOI : 10.1016/S0378-4371(98)00345-8

S. Kitsunezaki, Interface Dynamics for Bacterial Colony Formation, Journal of the Physical Society of Japan, vol.66, issue.5, pp.1544-1550, 1997.
DOI : 10.1143/JPSJ.66.1544

F. Hecht and A. Marrocco, Numerical simulation of heterojunction structures using mixed finite elements and operator splitting, 10th International Conference on Computing Methods in Applied Sciences and Engineering, pp.271-286, 1992.

F. Hecht and A. Marrocco, MIXED FINITE ELEMENT SIMULATION OF HETEROJUNCTION STRUCTURES INCLUDING A BOUNDARY LAYER MODEL FOR THE QUASI???FERMI LEVELS, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.13, issue.4, pp.757-770, 1994.
DOI : 10.1108/eb051893

A. El-boukili and A. Marrocco, Arclength continuation methods and applications to 2D drift???diffusion semiconductor equations, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.15, issue.4, 1995.
DOI : 10.1108/03321649610154203

URL : https://hal.archives-ouvertes.fr/inria-00074132

A. Boukili, Analyse mathématique et simulation numérique bidimensionnelle des dispositifs semiconducteursàconducteurs`conducteursà hétérojonctions par l'approché eléments finis mixtes, 1995.

F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Number 15 in Springer series in computational mathematics, 1991.

P. A. Raviart and J. M. Thomas, Mathematical aspects of the finite element method, chapter A mixed finite element method for second order elliptic problems. Number 606 in Lectures Notes in Math, 1977.

J. E. Roberts and J. M. Thomas, Handbook of Numerical Analysis, 1989.

R. Glowinski and P. Letallec, Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, Number 9 in Studies in Applied Mathematics. SIAM, Philadelphia, 1989.
DOI : 10.1137/1.9781611970838

A. Marrocco, . Ph, and . Montarnal, Simulation des modèles energy-transportàtransport`transportà l'aide desélémentsdeséléments finis mixtes, C.R. Acad. Sci. Paris, vol.323, pp.535-541, 1996.

. Ph, Modèles de transport d'´ energie des semi-conducteurs, ´ etudes asymptotiques et résolution par desélémentsdeséléments finis mixtes, 1997.

O. Schenck and K. Gärtner, Solving unsymmetric sparse systems of linear equations with PARDISO, Future Generation Computer Systems, vol.20, issue.3, pp.475-487, 2004.
DOI : 10.1016/j.future.2003.07.011

O. Schenck, K. Gärtner, and W. Fichtner, Efficient sparse LU factorization with left-right looking strategy on shared memory multiprocessors, Bit Numerical Mathematics, vol.40, issue.1, pp.158-176, 2000.
DOI : 10.1023/A:1022326604210

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