M. Alfaro and J. Coville, Rapid traveling waves in the nonlocal Fisher equation connect two unstable states, Applied Mathematics Letters, vol.25, issue.12, pp.2095-2099, 2012.
DOI : 10.1016/j.aml.2012.05.006

M. Alfaro, J. Coville, and G. , Travelling Waves in a Nonlocal Reaction-Diffusion Equation as a Model for a Population Structured by a Space Variable and a Phenotypic Trait, Communications in Partial Differential Equations, vol.19, issue.803, pp.2126-2154, 2013.
DOI : 10.1137/S0036144599364296

M. Alfaro, J. Coville, and G. , Bistable travelling waves for nonlocal reaction diffusion equations, Discrete Contin, Dyn. Syst. Ser. A, vol.34, pp.1775-1791, 2014.

D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Advances in Mathematics, vol.30, issue.1, pp.33-76, 1978.
DOI : 10.1016/0001-8708(78)90130-5
URL : http://doi.org/10.1016/0001-8708(78)90130-5

H. Berestycki, O. Diekmann, C. J. Nagelkerke, and P. A. Zegeling, Can a Species Keep Pace with a Shifting Climate?, Bulletin of Mathematical Biology, vol.45, issue.2, pp.399-429, 2009.
DOI : 10.1007/s11538-008-9367-5

H. Berestycki, F. Hamel, and L. Rossi, Liouville-type results for semilinear elliptic equations in unbounded domains, Annali di Matematica Pura ed Applicata, vol.24, issue.3, pp.469-507, 2007.
DOI : 10.1007/s10231-006-0015-0

H. Berestycki, T. Jin, and L. Silvestre, Propagation in a non local reaction diffusion equation with spatial and genetic trait structure, preprint arXiv:1411, 20192.

H. Berestycki, G. Nadin, B. Perthame, and L. Ryzhik, The non-local Fisher???KPP equation: travelling waves and steady states, Nonlinearity, vol.22, issue.12, pp.2813-2844, 2009.
DOI : 10.1088/0951-7715/22/12/002

H. Berestycki, L. Nirenberg, and S. R. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Communications on Pure and Applied Mathematics, vol.17, issue.1, pp.47-47, 1994.
DOI : 10.1002/cpa.3160470105

H. Berestycki and L. Rossi, Reaction-diffusion equations for population dynamics with forced speed. I. The case of the whole space, Discrete Contin, Dyn. Syst, vol.21, issue.1, pp.41-67, 2008.

H. Berestycki and L. Rossi, Reaction-diffusion equations for population dynamics with forced speed. II. Cylindrical-type domains, Discrete Contin, Dyn. Syst, vol.25, issue.1, pp.19-61, 2009.

M. D. Bramson, Maximal displacement of branching brownian motion, Communications on Pure and Applied Mathematics, vol.8, issue.5, pp.531-581, 1978.
DOI : 10.1002/cpa.3160310502

M. D. Bramson, Convergence of solutions of the Kolmogorov equation to travelling waves, Mem. Amer, Math. Soc, vol.44, 1983.

N. Champagnat and S. Méléard, Invasion and adaptive evolution for individual-based spatially structured populations, Journal of Mathematical Biology, vol.412, issue.3, pp.147-188, 2007.
DOI : 10.1007/s00285-007-0072-z
URL : https://hal.archives-ouvertes.fr/hal-00022153

A. Duputié, F. Massol, I. Chuine, M. Kirkpatrick, and O. Ronce, How do genetic correlations affect species range shifts in a changing environment?, Ecology Letters, vol.40, issue.3, pp.251-259, 2012.
DOI : 10.1111/j.1461-0248.2011.01734.x

L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, vol.19, 2010.

J. Fang and X. Zhao, Monotone wavefronts of the nonlocal Fisher???KPP equation, Nonlinearity, vol.24, issue.11, pp.3043-3054, 2011.
DOI : 10.1088/0951-7715/24/11/002

R. A. Fisher, THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES, Annals of Eugenics, vol.7, issue.4, pp.355-369, 1937.
DOI : 10.1111/j.1469-1809.1937.tb02153.x

S. Genieys, V. Volpert, and P. Auger, Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources, Mathematical Modelling of Natural Phenomena, vol.1, issue.1, pp.65-82, 2006.
DOI : 10.1051/mmnp:2006004

D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, 1977.

Q. Griette and G. , Existence and qualitative properties of travelling waves for an epidemiological model with mutations, preprint arXiv, pp.1412-6354

F. Hamel and L. Ryzhik, On the nonlocal Fisher???KPP equation: steady states, spreading speed and global bounds, Nonlinearity, vol.27, issue.11, pp.2735-2753, 2014.
DOI : 10.1088/0951-7715/27/11/2735
URL : https://hal.archives-ouvertes.fr/hal-00843279

M. Kirkpatrick and N. H. Barton, Evolution of a Species' Range, The American Naturalist, vol.150, issue.1, pp.1-23, 1997.
DOI : 10.1086/286054

A. N. Kolmogorov, I. G. Petrovsky, and N. S. Piskunov, Etude de l'´ equation de la diffusion avec croissance de la quantité dematì ere et son applicationàapplicationà unprobì eme biologique

G. M. Lieberman, Second Order Parabolic Differential Equations, 1996.
DOI : 10.1142/3302

S. Mirrahimi and G. , Dynamics of sexual populations structured by a space variable and a phenotypical trait, Theoretical Population Biology, vol.84, pp.87-103, 2013.
DOI : 10.1016/j.tpb.2012.12.003

J. Moser, A harnack inequality for parabolic differential equations, Communications on Pure and Applied Mathematics, vol.55, issue.1, pp.101-134, 1964.
DOI : 10.1002/cpa.3160170106

C. M. Pease, R. Lande, and J. J. Bull, A Model of Population Growth, Dispersal and Evolution in a Changing Environment, Ecology, vol.70, issue.6, pp.1657-1664, 1989.
DOI : 10.2307/1938100

J. Polechová, N. Barton, and G. Marion, Species' Range: Adaptation in Space and Time, The American Naturalist, vol.174, issue.5, pp.186-204, 2009.
DOI : 10.1086/605958

A. B. Potapov and M. A. Lewis, Climate and competition: the effect of moving range boundaries on habitat invasibility, Bulletin of Mathematical Biology, vol.66, issue.5, pp.975-1008, 2004.
DOI : 10.1016/j.bulm.2003.10.010

C. Prevost, Applications of partial differential equations and their numerical simulations of population dynamics, 2004.

O. Savolainen, T. Pyhäjärvi, and T. Knürr, Gene Flow and Local Adaptation in Trees, Annual Review of Ecology, Evolution, and Systematics, vol.38, issue.1, pp.595-619, 2007.
DOI : 10.1146/annurev.ecolsys.38.091206.095646

L. Schwartz, Analyse hilbertienne. Collection Methodes, 1979.