D. Adalsteinsson and J. A. Sethian, The Fast Construction of Extension Velocities in Level Set Methods, Journal of Computational Physics, vol.148, issue.1, pp.2-22, 1999.
DOI : 10.1006/jcph.1998.6090

N. R. Alexander, K. M. Branch, A. Parekh, E. S. Clark, I. C. Iwueke et al., Extracellular Matrix Rigidity Promotes Invadopodia Activity, Current Biology, vol.18, issue.17, pp.181295-1299, 2008.
DOI : 10.1016/j.cub.2008.07.090

URL : http://doi.org/10.1016/j.cub.2008.07.090

K. M. Branch, D. Hoshino, and A. M. Weaver, Adhesion rings surround invadopodia and promote maturation, Biology Open, vol.1, issue.8, p.20121867, 2012.
DOI : 10.1242/bio.20121867

URL : http://doi.org/10.1242/bio.20121867

M. Cisternino and L. Weynans, Abstract, Communications in Computational Physics, vol.39, issue.05, pp.1562-1587, 2012.
DOI : 10.1016/j.jcp.2006.02.014

H. Enderling, N. Alexander, E. S. Clark, K. M. Branch, L. Estrada et al., Dependence of Invadopodia Function on Collagen Fiber Spacing and Cross-Linking: Computational Modeling and Experimental Evidence, Biophysical Journal, vol.95, issue.5, pp.952203-2218, 2008.
DOI : 10.1529/biophysj.108.133199

R. P. Fedkiw, T. Aslam, B. Merriman, and S. Osher, A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method), Journal of Computational Physics, vol.152, issue.2, pp.457-492, 1999.
DOI : 10.1006/jcph.1999.6236

P. Friedl and K. Wolf, Tumour-cell invasion and migration: diversity and escape mechanisms, Nature Reviews Cancer, vol.3, issue.5, pp.362-374, 2003.
DOI : 10.1038/nrc1075

O. Gallinato and C. Poignard, Superconvergent second order Cartesian method for a free boundary model of invadopodia, 2016.

F. Gibou, R. P. Fedkiw, L. T. Cheng, and M. Kang, A Second-Order-Accurate Symmetric Discretization of the Poisson Equation on Irregular Domains, Journal of Computational Physics, vol.176, issue.1, pp.205-227, 2002.
DOI : 10.1006/jcph.2001.6977

M. Herant and M. Dembo, Form and Function in Cell Motility: From Fibroblasts to Keratocytes, Biophysical Journal, vol.98, issue.8, pp.1408-1417, 2010.
DOI : 10.1016/j.bpj.2009.12.4303

URL : http://doi.org/10.1016/j.bpj.2009.12.4303

W. R. Holmes and L. Edelstein-keshet, A Comparison of Computational Models for Eukaryotic Cell Shape and Motility, PLoS Computational Biology, vol.49, issue.19, p.1002793, 2012.
DOI : 10.1371/journal.pcbi.1002793.t001

D. Hoshino, N. Koshikawa, T. Suzuki, V. Quaranta, A. M. Weaver et al., Establishment and Validation of Computational Model for MT1-MMP Dependent ECM Degradation and Intervention Strategies, PLoS Computational Biology, vol.3, issue.4, pp.1-10, 2012.
DOI : 10.1371/journal.pcbi.1002479.s001

T. Iguchi, On the irrotational flow of incompressible ideal fluid in a circular domain with free surface, Publications of the Research Institute for Mathematical Sciences, vol.34, issue.6, pp.525-565, 1998.
DOI : 10.2977/prims/1195144422

T. Kato, Nonlinear semigroups and evolution equations, Journal of the Mathematical Society of Japan, vol.19, issue.4, pp.508-520, 1967.
DOI : 10.2969/jmsj/01940508

D. Lannes, Well-posedness of the water waves equations, J. Amer. Math. Soc, vol.18, issue.3, pp.605-654, 2005.
DOI : 10.1090/surv/188/04

URL : https://hal.archives-ouvertes.fr/hal-00258834

H. Levine and W. , The physics of eukaryotic chemotaxis, Physics Today, vol.66, issue.2, p.2013
DOI : 10.1063/PT.3.1884

P. Macklin and J. Lowengrub, Evolving interfaces via gradients of geometry-dependent interior Poisson problems: application to tumor growth, Journal of Computational Physics, vol.203, issue.1, pp.191-220, 2005.
DOI : 10.1016/j.jcp.2004.08.010

A. F. Marée, V. A. Grieneisen, and L. Edelstein-keshet, How Cells Integrate Complex Stimuli: The Effect of Feedback from Phosphoinositides and Cell Shape on Cell Polarization and Motility, PLoS Computational Biology, vol.86, issue.3, pp.1-20, 2012.
DOI : 10.1371/journal.pcbi.1002402.s010

A. F. Marée, A. Jilkine, A. Dawes, V. A. Grieneisen, and L. Edelstein-keshet, Polarization and Movement of Keratocytes: A Multiscale Modelling Approach, Bulletin of Mathematical Biology, vol.149, issue.4, pp.1169-1211, 2006.
DOI : 10.1007/s11538-006-9131-7

A. Mogilner, On the edge: modeling protrusion, Cell structure and dynamics, pp.32-39, 2006.
DOI : 10.1016/j.ceb.2005.11.001

V. I. Nalimov, The Cauchy-Poisson problem. Dinamika Splo?n. Sredy, Vyp. 18 Dinamika Zidkost. so Svobod, pp.104-210, 1974.

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

A. Pathak and S. Kumar, Biophysical regulation of tumor cell invasion: moving beyond matrix stiffness, Integrative Biology, vol.200, issue.4, pp.267-278, 2011.
DOI : 10.1089/ten.TEA.2010.0273

A. J. Ridley, M. A. Schwartz, K. Burridge, R. A. Firtel, M. H. Ginsberg et al., Cell Migration: Integrating Signals from Front to Back, Science, vol.302, issue.5651, pp.3021704-1709, 2003.
DOI : 10.1126/science.1092053

T. Saitou, M. Rouzimaimaiti, N. Koshikawa, M. Seiki, K. Ichikawa et al., Mathematical modeling of invadopodia formation, Journal of Theoretical Biology, vol.298, pp.138-146, 2012.
DOI : 10.1016/j.jtbi.2011.12.018

P. M. Schoumacher, R. D. Goldman, D. Louvard, and D. M. Vignjevic, Actin, microtubules, and vimentin intermediate filaments cooperate for elongation of invadopodia, The Journal of Cell Biology, vol.6, issue.3, pp.541-556, 2010.
DOI : 10.1002/cbf.1478

G. H. Shortley and R. Weller, The Numerical Solution of Laplace's Equation, Journal of Applied Physics, vol.9, issue.5, p.334, 1938.
DOI : 10.1063/1.1710426

C. Stock and A. Schwab, Role of the Na+/H+ exchanger NHE1 in cell migration, Acta Physiologica, vol.276, issue.1, pp.149-157, 2006.
DOI : 10.1002/(SICI)1097-4652(200007)184:1<118::AID-JCP13>3.3.CO;2-P

D. Strychalski, W. Adalsteinsson, and T. C. Elston, Simulating Biochemical Signaling Networks in Complex Moving Geometries, SIAM Journal on Scientific Computing, vol.32, issue.5, pp.3039-3070, 2010.
DOI : 10.1137/090779693

R. F. Warming and R. M. Beam, Upwind second-order difference schemes and applications in aerodynamic flows, AIAA Journal, vol.14, issue.907, pp.1241-1249, 1976.

C. Wolgemuth, J. Stajic, and A. Mogilner, Redundant Mechanisms for Stable Cell Locomotion Revealed by Minimal Models, Biophysical Journal, vol.101, issue.3, pp.545-553, 2011.
DOI : 10.1016/j.bpj.2011.06.032

M. Yang, D. J. Kozminski, L. A. Wold, R. Modak, J. D. Calhoun et al., Therapeutic potential for phenytoin: targeting Nav1.5 sodium channels to reduce migration and invasion in metastatic breast cancer, Breast Cancer Research and Treatment, vol.221, issue.4, pp.603-615, 2012.
DOI : 10.1007/s10549-012-2102-9

H. Yosihara, Gravity waves on the free surface of an incompressible perfect fluid of finite depth, Publications of the Research Institute for Mathematical Sciences, vol.18, issue.1, pp.49-96, 1982.
DOI : 10.2977/prims/1195184016