O. Alvarez, J. Lasry, and P. Lions, Convex viscosity solutions and state constraints, J. Math. Pures Appl, vol.76, issue.3, pp.265-288, 1997.

S. Armstrong and P. E. Souganidis, Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments, J. Math. Pures Appl, vol.97, issue.5, pp.460-504, 2012.

S. Armstrong and H. V. Tran, Viscosity solutions of general viscous Hamilton-Jacobi equations, Math. Ann, vol.361, issue.3-4, pp.647-687, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00903281

D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusions arising in population genetics, Adv. Math, vol.30, pp.33-76, 1978.

G. Barles and E. Chasseigne, Almost) Everything You Always Wanted to Know About Deterministic Control Problems in Stratified Domains, Networks and Heterogeneous Media, vol.10, issue.4, pp.809-836, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01097167

G. Barles and B. Perthame, Exit time problems in optimal control and vanishing viscosity method, SIAM J. Control Optim, vol.26, issue.5, pp.1133-1148, 1988.

G. Barles and B. Perthame, Discontinuous solutions of deterministic optimal stopping time problems, RAIRO Modél. Math. Anal. Numér, vol.21, issue.4, pp.557-579, 1987.

H. Berestycki and F. Hamel, Reaction-DIffusion Equations and Propagation Phenomena

H. Berestycki and F. Hamel, Front propagation in periodic excitable media, Comm. Pure Appl. Math, vol.55, pp.949-1032, 2002.

H. Berestycki and F. Hamel, Generalized traveling waves for reaction-diffusion equations. Perspectives in Nonlinear Partial Differential Equations. In honor of H. Brezis, Amer. Math. Soc, vol.446, pp.101-123, 2007.

H. Berestycki and F. Hamel, Generalized transition waves and their properties, Communications on Pure and Applied Mathematics, vol.65, issue.5, pp.592-648, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00505135

H. Berestycki, F. Hamel, and H. Matano, Bistable traveling waves around an obstacle, Comm. Pure Appl. Math, vol.62, pp.729-788, 2009.

H. Berestycki, F. Hamel, and G. Nadin, Asymptotic spreading in heterogeneous diffusive excitable media, J. Func. Anal, vol.255, issue.9, pp.2146-2189, 2008.

H. Berestycki, F. Hamel, and N. Nadirashvili, Propagation speed for reaction-diffusion equations in general domains, C.R. Acad. Sci. Paris Ser. I, vol.339, pp.163-168, 2004.

H. Berestycki, F. Hamel, and N. Nadirashvili, The speed of propagation for KPP type problems. I -Periodic framework, J. European Math. Soc, vol.7, pp.173-213, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00003805

H. Berestycki, F. Hamel, and N. Nadirashvili, The speed of propagation for KPP type problems. II -General domains, J. Amer. Math. Soc, vol.23, pp.1-34, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00003805

H. Berestycki, F. Hamel, and L. Roques, Analysis of the periodically fragmented environment model : II -biological invasions and pulsating traveling fronts, J. Math. Pures Appl, vol.84, pp.1101-1146, 2005.

H. Berestycki, F. Hamel, and L. Rossi, Liouville-type results for semilinear elliptic equations in unbounded domains, Ann. Mat. Pura Appl, vol.186, issue.4, pp.469-507, 2007.

H. Berestycki and G. Nadin, Spreading speeds for one-dimensional monostable reactiondiffusion equations, J. Math. Phys, vol.53, issue.11, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01080135

H. Berestycki, G. Nadin, and L. Rossi, Generalized principal eigenvalues for parabolic operators

H. Berestycki, L. Nirenberg, and S. R. Varadhan, The principal eigenvalue and maximum principle for second order elliptic operators in general domains, Comm. Pure Appl. Math, vol.47, pp.47-92, 1994.

H. Berestycki, J. Roquejoffre, and L. Rossi, The shape of expansion induced by a line with fast diffusion in Fisher-KPP equations, Communications in Mathematical Physics, vol.343, issue.1, pp.7-232, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01978596

H. Berestycki and L. Rossi, On the principal eigenvalue of elliptic operators in R N and applications, J. European Math. Soc, vol.8, pp.195-215, 2006.

H. Berestycki and L. Rossi, Generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains, Com. Pure Appl. Math, vol.68, issue.6, pp.1014-1065, 2015.

J. Berestycki, E. Brunet, and B. Derrida, Exact solution and precise asymptotics of a Fisher-KPP type front, Journal of Physics A: Mathematical and Theoretical, vol.51, issue.3, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01723857

J. Berestycki, E. Brunet, S. C. Harris, and M. Roberts, Vanishing corrections for the position in a linear model of FKPP fronts, Comm. Math. Phys, vol.349, issue.3, 2017.

K. Bjerklov, Positive Lyapunov exponents for continuous quasiperiodic Schrodinger equations, J. Math. Phys, vol.47, 2006.

S. Bochner, Beitrage zur theorie der fastperiodischen funktionen, Math. Ann, vol.96, pp.119-147, 1926.

M. Bramson, Convergence of solutions of the Kolmogorov equation to traveling waves, Mem. Amer. Math. Soc, vol.44, issue.285, 1983.

E. Brunet, B. Derrida, A. H. Mueller, and S. Munier, Phenomenological theory giving the full statistics of the position of fluctuating pulled fronts, Phys. Rev. E, vol.73, p.56126, 2006.

P. Cardaliaguet and P. Souganidis, On the existence of correctors for the stochastic homogenization of viscous Hamilton-Jacobi equations, C.R. Acad. Sci. Paris, Ser.I, vol.355, pp.786-794, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01513374

G. Cole, Precise asymptotics for Fisher-KPP fronts, 2017.

M. G. Crandall, H. Ishii, and P. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc, vol.27, pp.1-67, 1992.

M. G. Crandall and P. Lions, Viscosity Solutions of Hamilton-Jacobi Equations, Trans. Amer. Math. Soc, vol.277, issue.1, pp.1-42, 1983.

A. Davini and A. Siconolfi, Exact and approximate correctors for stochastic Hamiltonians: the 1-dimensional case, Math. Annal, vol.345, issue.4, pp.749-782, 2009.

R. Ducasse, Influence of the geometry on a field-road model : the case of a conical field, Journal of the London Mathematical Society, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01517063

L. C. Evans, Periodic homogenization of certain fully nonlinear partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A, vol.120, pp.245-265, 1992.

L. C. Evans and P. E. Souganidis, A PDE approach to geometric optics for certain semilinear parabolic equations, Indiana Univ. Math, vol.38, issue.1, pp.141-172, 1989.

R. A. Fisher, The advance of advantageous genes, Ann. Eugenics, vol.7, pp.335-369, 1937.

M. Freidlin, Limit Theorems for Large Deviations and Reaction-Diffusion Equations, Ann. Probab, vol.13, issue.3, pp.639-675, 1985.

M. Freidlin, On wave front propagation in periodic media, Advances in Probability and related topics, vol.7, pp.147-166, 1984.

M. Freidlin and J. Gärtner, On the propagation of concentration waves in periodic and random media, Sov. Math. Dokl, vol.20, pp.1282-1286, 1979.

M. Freidlin and T. Lee, Wave front propagation and large deviations for diffusiontransmutation process, Probab. Theory Relat. Fields, vol.106, pp.39-70, 1996.

J. Garnier, T. Giletti, and G. Nadin, Maximal and minimal spreading speeds for reaction diffusion equations in nonperiodic slowly varying media, J. Dynam. Differential Equations, vol.24, issue.3, pp.521-538, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00939216

Y. Giga, P. Gorka, and P. Rybka, A comparison principle for Hamilton-Jacobi equations with discontinuous Hamiltonians, Proc. Amer. Math. Soc, vol.139, issue.5, pp.1777-1785, 2011.

F. Hamel, J. Nolen, J. Roquejoffre, and L. Ryzhik, A short proof of the logarithmic Bramson correction in Fisher-KPP equations, Netw. Heterog. Media, vol.8, issue.1, pp.275-289, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00815553

F. Hamel, J. Nolen, J. Roquejoffre, and L. Ryzhik, The logarithmic delay of KPP fronts in a periodic medium, 2012.
URL : https://hal.archives-ouvertes.fr/hal-02077815

J. Húska, P. Polá?ik, and M. V. Safonov, Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.24, issue.5, pp.711-739, 2007.

J. Húska and P. Polá?ik, Exponential separation and principal Floquet bundles for linear parabolic equations on R N . Discrete and Continuous Dynamical Systems -A, vol.20, pp.81-113, 2008.

C. Imbert, Convexity of solutions and C 1,1 estimates for fully nonlinear elliptic equations, J. Math. Pures et Appl, vol.85, issue.6, pp.791-807, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00012969

C. Imbert and R. Monneau, Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks, Annales Scientifiques de l?ENS, vol.50, issue.2, pp.357-448, 2017.
URL : https://hal.archives-ouvertes.fr/hal-00832545

C. Imbert and R. Monneau, Quasi-convex Hamilton-Jacobi equations posed on junctions: the multi-dimensional case. Discrete and continuous dynamical systems ? series A, vol.37, pp.6405-6435, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01073954

H. Ishii, Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets, Bull. Fac. Sci. Engrg. Chuo Univ, vol.28, pp.33-77, 1985.

H. Ishii, Perron's method for Hamilton-Jacobi equations, Duke Math. J, vol.55, issue.2, pp.369-384, 1987.

H. Ishii, A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.16, issue.1, pp.105-135, 1989.

H. Ishii, Homogenization of the Cauchy problem for Hamilton-Jacobi equations. Stochastic analysis, control, optimization and applications, Systems Control Found. Appl, pp.305-324, 1999.

A. N. Kolmogorov, I. G. Petrovsky, and N. S. Piskunov, Etude de léquation de la diffusion avec croissance de la quantité de matière et son applicationà un problème biologique, pp.1-26, 1937.

L. Kong and W. Shen, Positive Stationary Solutions and Spreading Speeds of KPP Equations in Locally Spatially Inhomogeneous Media, Methods and Applications of Analysis, vol.18, pp.427-456, 2011.

E. Kosygina, F. Rezakhanlou, and S. R. Varadhan, Stochastic homogenization of Hamilton-Jacobi-Bellman Equations, Communications on Pure and Applied Mathematics, vol.59, issue.10, pp.1489-1521, 2006.

E. Kosygina and S. R. Varadhan, Homogenization of Hamilton-Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium, Communications on Pure and Applied Mathematics, vol.61, issue.6, pp.816-847, 2008.

S. M. Kozlov, Ground states of quasiperiodic operators, Dokl. Akad. Nauk SSSR, vol.271, issue.3, pp.532-536, 1983.

B. M. Levitan, Almost periodic functions and differential equations, 1982.

B. Lewin and B. Lewitan, On the Fourier series of generalized almost periodic functions. Comptes-rendus (Doklady) de l'Académie des, Sciences de l'URSS, vol.22, issue.9, pp.539-542, 1939.

P. Lions, G. Papanicolaou, and S. R. Varadhan, Homogenization of HamiltonJacobi equations. Unpublished, circa, 1988.
URL : https://hal.archives-ouvertes.fr/hal-00667310

P. Lions and P. E. Souganidis, Correctors for the homogenization theory of HamiltonJacobi equations, Comm Pure Applied Math, vol.LVI, pp.1501-1524, 2003.

P. Lions and P. E. Souganidis, Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications, Ann. Inst. H. Poincare, Anal. Non Linéaire, vol.22, issue.5, pp.667-677, 2005.

P. Lions and P. E. Souganidis, Homogenization of "viscous" Hamilton-Jacobi equations in stationary ergodic media, Comm. Partial Differential Equations, vol.30, issue.1-3, pp.335-375, 2005.

R. Lions and P. E. Souganidis, Stochastic homogenization of Hamilton-Jacobi and "viscous"-Hamilton-Jacobi equations with convex nonlinearities?revisited, Commun. Math. Sci, vol.8, issue.2, pp.627-637, 2010.

A. J. Majda and P. E. Souganidis, Large-scale front dynamics for turbulent reactiondiffusion equations with separated velocity scales, Nonlinearity, vol.7, issue.1, pp.1-30, 1994.

H. Matano, Traveling waves in spatially random media, RIMS Kokyuroku, vol.1337, pp.1-9, 2003.

H. Matano and M. Nara, Large time behavior of disturbed planar fronts in the AllenCahn equation, J. Differential Equations, issue.12, pp.3522-3557, 2011.

A. Mellet, J. Nolen, J. Roquejoffre, and L. Ryzhik, Stability of generalized transitions fronts, Comm. Partial Differential Equations, vol.34, pp.521-552, 2009.

A. Mellet, J. Roquejoffre, and Y. Sire, Generalized fronts for one-dimensionnal reaction-diffusion equations, Discrete Contin. Dyn. Syst, vol.26, issue.1, pp.303-312, 2009.

G. Nadin, Traveling fronts in space-time periodic media, J. Math. Pures Appl, vol.92, pp.232-262, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01360584

G. Nadin and L. Rossi, Propagation phenomena for time heterogeneous KPP reactiondiffusion equations, J. Math. Pures Appl, vol.98, issue.9, pp.633-653, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01080139

G. Nadin and L. Rossi, Transition waves for Fisher-KPP equations with general timeheterogeneous et space-periodic coefficients, Analysis and PDE, vol.8, issue.6, pp.1351-1377, 2015.

G. Nadin and L. Rossi, Generalized transition fronts for one-dimensional almost periodic Fisher-KPP equations, Arch. Rat. Mec. Anal, vol.223, issue.3, pp.1239-1267, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01226854

J. Nolen, J. Roquejoffre, L. Ryzhik, and A. Zlato?, Existence and non-existence of Fisher-KPP transition fronts, Arch. Rat. Mec. Anal, vol.203, issue.1, pp.217-246, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00942886

J. Nolen, M. Rudd, and J. Xin, Existence of KPP fronts in spatially-temporally periodic advection and variational principle for propagation speeds, Dynamics of PDE, vol.2, issue.1, pp.1-24, 2005.

J. Nolen and L. Ryzhik, Traveling waves in a one-dimensional heterogeneous medium, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.26, issue.3, pp.1021-1047, 2009.

J. Nolen and J. Xin, Asymptotic Spreading of KPP Reactive Fronts in Incompressible Space-Time Random Flows. Ann. de l'Inst. Henri Poincare -Analyse Non Lineaire, vol.26, pp.815-839, 2008.

J. Nolen and J. Xin, KPP Fronts in 1D Random Drift. Discrete and Continuous Dynamical Systems B, vol.11, 2009.

J. Nolen and J. Xin, Variational Principle of KPP Front Speeds in Temporally Random Shear Flows with Applications, Communications in Mathematical Physics, vol.269, pp.493-532, 2007.

G. C. Papanicolaou and S. R. Varadhan, Boundary value problems with rapidly oscillating random coefficients, Proceedings of Conference on Random Fields, Esztergom, vol.27, pp.835-873, 1979.

E. A. Robinson, The dynamical properties of Penrose tilings, Trans AMS, vol.348, pp.4447-4464, 1996.

L. Rossi, Liouville type results for periodic and almost periodic linear operators, Ann. I. H. Poincaré -AN, vol.26, pp.2481-2502, 2009.

L. Rossi and L. Ryzhik, Transition waves for a class of space-time dependent monostable equations, Commun. Math. Sci, vol.12, issue.5, pp.879-900, 2014.

R. Schwab, Stochastic Homogenization of Hamilton-Jacobi Equations in Stationary Ergodic Spatio-Temporal Media, Indiana Univ. Math. J, vol.58, issue.2, pp.537-581, 2009.

B. Shabani, Propagation in multi-dimensional Fisher-KPP equations, 2017.

W. Shen, traveling waves in time almost periodic structures governed by bistable nonlinearities. I. Stability and uniqueness, J. Differential Equations, vol.159, issue.1, pp.1-54, 1999.

W. Shen, traveling waves in time almost periodic structures governed by bistable nonlinearities, II. Existence. J. Differential Equations, vol.159, issue.1, pp.55-101, 1999.

W. Shen, Traveling waves in diffusive random media, J. Dynam. Differential Equations, vol.16, issue.4, pp.1011-1060, 2004.

W. Shen, Traveling waves in time dependent bistable equations. Differential Integral Equations, vol.19, pp.241-278, 2006.

W. Shen, Variational principle for spatial spreading speeds and generalized propagating speeds in time almost periodic and space periodic KPP models, Transactions of the American Mathematical Society, vol.362, pp.5125-5168, 2010.

W. Shen, Existence, uniqueness, and stability of generalized traveling waves in time dependent monostable equations, J. Dynam. Differential Equations, vol.23, issue.1, pp.1-44, 2011.

J. G. Skellam, Random Dispersal in Theoretical Populations, Biometrika, vol.38, pp.196-218, 1951.

P. Soravia, Boundary value problems for Hamilton-Jacobi equations with discontinuous Lagrangian, Indiana Univ. Math. J, vol.51, issue.2, pp.451-477, 2002.

E. Sorets and T. Spencer, Positive Lyapunov Exponents for Schrodinger Operators with Quasi-Periodic Potentials Commun, Math. Phys, vol.142, pp.543-566, 1991.

P. E. Souganidis, Stochastic homogenization of Hamilton-Jacobi equations and some applications, Asymptot. Anal, vol.20, issue.1, pp.1-11, 1999.

A. Tourin, A comparison theorem for a piecewise Lipschitz continuous Hamiltonian and application to Shape-from-Shading problems, Numerische Mathematik, vol.62, issue.1, pp.75-85, 1992.

W. A. Veech, On a Theorem of Bochner, Ann. Math, vol.86, 1967.

H. Weinberger, On spreading speed and traveling waves for growth and migration models in a periodic habitat, J. Math. Biol, vol.45, pp.511-548, 2002.

G. Wulff, Zur Frage der Geschwindigkeit des Wachstums und der Auflösung der Krystallflagen, Z. Kryst. Mineral, vol.34, p.449, 1901.

J. Xin, Front propagation in heterogeneous media, SIAM Rev, vol.42, pp.161-230, 2000.

A. Zlato?, Transition fronts in inhomogeneous Fisher-KPP reaction-diffusion equations, J. Math. Pures Appl, vol.98, pp.89-102, 2012.

A. Zlato?, Generalized traveling waves in disordered media: existence, uniqueness, and stability, Arch. Ration. Mech. Anal, vol.208, issue.2, pp.447-480, 2013.

A. Zlato?, Propagation of reactions in inhomogeneous media, Comm. Pure Appl. Math, vol.70, pp.884-949, 2017.

. B. Ya, D. Zeldovich, and . Frank-kamenetskii, A theory of thermal flame propagation, Acta Physicochimica URSS, vol.IX, issue.12, p.350, 1938.