Existence, uniqueness and regularity for nonlinear degenerate parabolic equations with nonlocal terms ,
Existence and uniqueness for dislocation dynamics with nonnegative velocity, Interfaces and Free Boundaries, vol.7, pp.415-434, 2005. ,
DOI : 10.4171/IFB/131
R??solution en temps court d'une ??quation de Hamilton???Jacobi non??locale d??crivant la dynamique d'une dislocation, Comptes Rendus Mathematique, vol.338, issue.9, pp.679-684, 2004. ,
DOI : 10.1016/j.crma.2004.03.007
Dislocation Dynamics: Short-time Existence and Uniqueness of the Solution, Archive for Rational Mechanics and Analysis, vol.51, issue.3, pp.449-504, 2006. ,
DOI : 10.1007/s00205-006-0418-5
Solutions de viscosité deséquationsdeséquations de Hamilton-Jacobi, 1994. ,
A new stability result for viscosity solutions of nonlinear parabolic equations with weak convergence in time, Comptes Rendus Mathematique, vol.343, issue.3, pp.173-178, 2006. ,
DOI : 10.1016/j.crma.2006.06.022
URL : https://hal.archives-ouvertes.fr/hal-00016437
Global Existence Results and Uniqueness for Dislocation Equations, SIAM Journal on Mathematical Analysis, vol.40, issue.1 ,
DOI : 10.1137/070682083
URL : https://hal.archives-ouvertes.fr/hal-00129352
In preparation, 2007. ,
Nonlocal First-Order Hamilton???Jacobi Equations Modelling Dislocations Dynamics, Communications in Partial Differential Equations, vol.6, issue.8, pp.311191-1208, 2006. ,
DOI : 10.1007/BFb0094298
URL : https://hal.archives-ouvertes.fr/hal-00021694
Front Propagation and Phase Field Theory, SIAM Journal on Control and Optimization, vol.31, issue.2, pp.439-469, 1993. ,
DOI : 10.1137/0331021
Vicosity solutions of fully nonlinear second order parabolic equations with L 1 -time dependence and Neumann boundary conditions ,
Vicosity solutions of fully nonlinear second order parabolic equations with L 1 -time dependence and Neumann boundary conditions. existence and applications to the level-set approach ,
Interior sphere property of attainable sets and time optimal control problems, ESAIM: Control, Optimisation and Calculus of Variations, vol.12, issue.2, pp.350-370, 2006. ,
DOI : 10.1051/cocv:2006002
On front propagation problems with nonlocal terms, Adv. Differential Equations, vol.5, issue.1-3, pp.213-268, 2000. ,
Front propagation problems with nonlocal terms. II, J. Math. Anal. Appl, vol.260, issue.2, pp.572-601, 2001. ,
Regularity of the Eikonal Equation with Neumann Boundary Conditions in the Plane: Application to Fronts with Nonlocal Terms, SIAM Journal on Control and Optimization, vol.45, issue.3, pp.1017-1038, 2006. ,
DOI : 10.1137/050635894
Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, Journal of Differential Geometry, vol.33, issue.3, pp.749-786, 1991. ,
DOI : 10.4310/jdg/1214446564
Viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society, vol.277, issue.1, pp.1-42, 1983. ,
DOI : 10.1090/S0002-9947-1983-0690039-8
Nonlocal front propagation problems in bounded domains with Neumann-type boundary conditions and applications, Asymptot . Anal, vol.37, pp.3-4257, 2004. ,
Motion of level sets by mean curvature. I, Journal of Differential Geometry, vol.33, issue.3, pp.635-681, 1991. ,
DOI : 10.4310/jdg/1214446559
Surface evolution equations, Monographs in Mathematics. Birkhäuser Verlag, vol.99, 2006. ,
Global Existence of Weak Solutions for Interface Equations Coupled with Diffusion Equations, SIAM Journal on Mathematical Analysis, vol.23, issue.4, pp.821-835, 1992. ,
DOI : 10.1137/0523043
Theory of dislocations, 1992. ,
Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets, Bull. Fac. Sci. Eng. Chuo Univ, vol.28, pp.33-77, 1985. ,
Lower-bound gradient estimates for first-order Hamilton-Jacobi equations and applications to the regularity of propagating fronts, Adv. Differential Equations, vol.6, issue.5, pp.547-576, 2001. ,
Theory of crystal dislocations, 1969. ,
Uniqueness of viscosity solutions of fully nonlinear second order parabolic equations with discontinuous time-dependence, Differential Integral Equations, vol.3, issue.1, pp.77-91, 1990. ,
Existence and uniqueness of unbounded viscosity solutions of parabolic equations with discontinuous time-dependence, Nonlinear Analysis: Theory, Methods & Applications, vol.18, issue.11, pp.1033-1062, 1992. ,
DOI : 10.1016/0362-546X(92)90194-J
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
Phase field methods and dislocations, Acta Materialia, vol.51, issue.1, pp.17-30, 2003. ,
DOI : 10.1016/S1359-6454(01)00379-2
URL : https://hal.archives-ouvertes.fr/hal-00125516
Approximation schemes for propagation of fronts with nonlocal velocities and Neumann boundary conditions, Nonlinear Analysis: Theory, Methods & Applications, vol.52, issue.1, pp.79-115, 2003. ,
DOI : 10.1016/S0362-546X(02)00098-6
Phase-Field Theory for FitzHugh???Nagumo-Type Systems, SIAM Journal on Mathematical Analysis, vol.27, issue.5, pp.1341-1359, 1996. ,
DOI : 10.1137/S0036141094261318
Nonlocal second-order Hamilton-Jacobi equations arising in tomographic reconstruction. submitted, 2006. ,