M. Bardi and I. Capuzzo-dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi- Bellman equations. Systems & Control: Foundations & Applications, With appendices by Maurizio Falcone and Pierpaolo Soravia, 1997.

G. Barles, Solutions de viscosité deséquationsdeséquations de Hamilton-Jacobi, of Mathématiques & Applications (Berlin) [Mathematics & Applications, 1994.

G. Barles, Discontinuous viscosity solutions of first-order Hamilton-Jacobi equations: a guided visit, Nonlinear Analysis: Theory, Methods & Applications, vol.20, issue.9, pp.1123-1134, 1993.
DOI : 10.1016/0362-546X(93)90098-D

G. Barles, L. C. Evans, and P. E. Souganidis, Wavefront propagation for reaction-diffusion systems of PDE. Duke Math, J, vol.61, issue.3, pp.835-858, 1990.

G. Barles, S. Mirrahimi, and B. Perthame, Concentration in Lotka-Volterra Parabolic or Integral Equations: A General Convergence Result, Methods and Applications of Analysis, vol.16, issue.3, pp.321-340, 2009.
DOI : 10.4310/MAA.2009.v16.n3.a4

URL : https://hal.archives-ouvertes.fr/hal-00391982

G. Barles and B. Perthame, Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics, Contemp. Math, vol.439, pp.57-68, 2007.
DOI : 10.1090/conm/439/08463

E. N. Barron and R. Jensen, Semicontinuous Viscosity Solutions For Hamilton???Jacobi Equations With Convex Hamiltonians, Communications in Partial Differential Equations, vol.10, issue.12, pp.1713-1742, 1990.
DOI : 10.1007/BF02765025

P. Cardaliaguet, A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable, ESAIM: Control, Optimisation and Calculus of Variations, vol.15, issue.2, pp.367-376, 2009.
DOI : 10.1051/cocv:2008028

URL : https://hal.archives-ouvertes.fr/hal-00258297

M. G. Crandall, H. Ishii, and P. Lions, user's guide to viscosity solutions\\ of second order\\ partial differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992.
DOI : 10.1090/S0273-0979-1992-00266-5

M. G. Crandall and P. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc, issue.1, pp.1-42, 1983.

L. C. Evans and B. K. Knerr, Instantaneous shrinking of the support of nonnegative solutions to certain nonlinear parabolic equations and variational inequalities, Illinois J. Math, vol.23, issue.1, pp.153-166, 1979.

W. H. Fleming and H. M. Soner, Controlled Markov processes and viscosity solutions, volume 25 of Stochastic Modelling and Applied Probability, 2006.

M. Gauduchon and B. Perthame, Survival thresholds and mortality rates in adaptive dynamics: conciliating deterministic and stochastic simulations, Mathematical Medicine and Biology, vol.27, issue.3, pp.195-210, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00755201

P. L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics, vol.69, 1982.

B. Perthame and G. Barles, Dirac concentrations in Lotka-Volterra parabolic PDEs, Indiana University Mathematics Journal, vol.57, issue.7, pp.3275-3301, 2008.
DOI : 10.1512/iumj.2008.57.3398

URL : https://hal.archives-ouvertes.fr/hal-00168404

P. Quittner and P. Souplet, Superlinear parabolic problems. Blow-up, global existence and steady state. Birkhäuser Advanced texts, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00094744

H. M. Soner, Optimal Control with State-Space Constraint I, SIAM Journal on Control and Optimization, vol.24, issue.3, pp.552-561, 1986.
DOI : 10.1137/0324032

P. E. Souganidis, Front propagation: Theory and applications, Viscosity solutions and applications, pp.186-242, 1995.
DOI : 10.1007/BF01049962