M. B. Amar and A. Goriely, Growth and instability in elastic tissues, Journal of the Mechanics and Physics of Solids, vol.53, issue.10, pp.2284-2319, 2005.
DOI : 10.1016/j.jmps.2005.04.008

H. Berestycki, B. Nicolaenko, and B. Scheurer, Traveling Wave Solutions to Combustion Models and Their Singular Limits, SIAM Journal on Mathematical Analysis, vol.16, issue.6, pp.1207-1242, 1985.
DOI : 10.1137/0516088

H. Berestycki, S. Terracini, K. Wang, and J. Wei, On entire solutions of an elliptic system modeling phase separations, Advances in Mathematics, vol.243, pp.102-126, 2013.
DOI : 10.1016/j.aim.2013.04.012

J. Billingham and D. J. Needham, The Development of Travelling Waves in Quadratic and Cubic Autocatalysis with Unequal Diffusion Rates. I. Permanent Form Travelling Waves, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.334, issue.1633, pp.3341-3365, 1633.
DOI : 10.1098/rsta.1991.0001

X. Chen and M. Taniguchi, Instability of spherical interfaces in a nonlinear free boundary problem, Adv. Differential Equations, vol.5, issue.4-6, pp.747-772, 2000.

P. Ciarletta, L. Foret, and M. B. Amar, The radial growth phase of malignant melanoma: multi-phase modelling, numerical simulations and linear stability analysis, Journal of The Royal Society Interface, vol.35, issue.2, pp.345-368, 2011.
DOI : 10.1016/j.compbiomed.2003.11.004

I. Golding, Y. Kozlovsky, I. Cohen, and E. B. 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

F. Hamel and L. Ryzhik, Traveling Fronts for the Thermo-Diffusive System with Arbitrary Lewis Numbers, Archive for Rational Mechanics and Analysis, vol.4, issue.4, pp.923-952, 2010.
DOI : 10.1007/s00205-009-0234-9

F. Hecht, New development in freefem++, Journal of Numerical Mathematics, vol.20, issue.3-4, pp.251-265, 2012.
DOI : 10.1515/jnum-2012-0013

D. A. Kessler and H. Levine, Fluctuation-induced diffusive instabilities. Letters to Nature, pp.556-558, 1998.

M. Marion, Qualitative properties of a nonlinear system for laminar flames without ignition temperature, Nonlinear Analysis: Theory, Methods & Applications, vol.9, issue.11, pp.1269-1292, 1985.
DOI : 10.1016/0362-546X(85)90035-5

URL : https://hal.archives-ouvertes.fr/inria-00076264

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

F. Beno??tbeno??t-perthame, J. L. Quirós, and . Vázquez, The hele-shaw asymptotics for mechanical models of tumor growth

D. H. Sattinger, On the stability of waves of nonlinear parabolic systems, Advances in Mathematics, vol.22, issue.3, pp.312-355, 1976.
DOI : 10.1016/0001-8708(76)90098-0

J. A. Sherratt and M. A. Chaplain, A new mathematical model for avascular tumour growth, Journal of Mathematical Biology, vol.43, issue.4, pp.291-312, 2001.
DOI : 10.1007/s002850100088

M. Taniguchi, Instability of planar traveling waves in bistable reaction-diffusion systems, Discrete and Continuous Dynamical Systems - Series B, vol.3, issue.1, pp.21-44, 2003.
DOI : 10.3934/dcdsb.2003.3.21

M. Taniguchi and Y. Nishiura, Instability of Planar Interfaces in Reaction-Diffusion Systems, SIAM Journal on Mathematical Analysis, vol.25, issue.1, pp.99-134, 1994.
DOI : 10.1137/S0036141092233500

I. Aizik, . Volpert, A. Vitaly, V. A. Volpert, and . Volpert, Traveling wave solutions of parabolic systems, volume 140 of Translations of Mathematical Monographs, 1994.