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- O. Alvarez, P. Hoch, Y. Le Bouar and R. Monneau, "Existence et
unicité en temps court d'une solution
de viscosité discontinue d'une équation de Hamilton-Jacobi non locale décrivant la dynamique d'une dislocation", Note C.R. Acad. Sci. Paris, Ser. I 338 (2004) 679-684.
- A. Ghorbel and R. Monneau, "Equation d'Hamilton-Jacobi non-locale modélisant la dynamique des dislocations" , Proceedings of the Conference:
Tendances des Applications Mathématiques en Tunisie, Algérie, Maroc 2005,
Ed. ENIT-LAMSIN, 322-328 (2005).
-
O.Alvarez, E.Carlini, P.Hoch, Y.Le Bouar and R. Monneau, "Dislocation
dynamics described by
non-local Hamilton-Jacobi equations", Materials Science & Engineering: A , Volumes 400-401, 25 July 2005,
pages 162-165.
- O.Alvarez, P. Cardaliaguet and R. Monneau,
,
"Existence and uniqueness for dislocation dynamics with nonnegative
velocity", Interfaces and Free Boundaries, 7 (4), 415-434, (2005).
- O.Alvarez, P.Hoch, Y.Le Bouar and R. Monneau,
Dislocation dynamics: short time existence and uniqueness of the
solution,
Archive for Rational Mechanics and Analysis, 181 (3),
449-504, (2006).
- O. Alvarez, E. Carlini, R. Monneau and E. Rouy,
Convergence
of a first order scheme for a non local eikonal equation,
Numerical Mathematics, 56, 2006, 1136-1146.
- O. Alvarez, E. Carlini, R. Monneau and E. Rouy,
A
convergent scheme for a non local
Hamilton Jacobi equation modelling
dislocation dynamics, Numerische Mathematik, Volume 104, Number 4,
pages 413-444.
- P. Cardaliaguet, F. Da Lio, N. Forcadel and R. Monneau,
Dislocation
dynamics : a non-local moving boundary, proceedings du congres FBP
2005, Coimbra, Portugal, International Series of Numerical Mathematics,
Vol. 154,
Birkhaüser Verlag Basel/Switzerland, 125-135, (2006).
- E. Carlini, E. Cristiani and N. Forcadel,
A non-monotone Fast Marching scheme for a Hamilton-Jacobi equation
modeling dislocation dynamics,
Numerical Mathematics and Advanced Applications Proceedings of
ENUMATH 2005
the 6th European Conference on Numerical Mathematics and Advanced
Applications, Santiago
de Compostela, Spain, July 2005 Bermdez de Castro,
A.; Gmez, D.; Quintela, P.; Salgado, P. (Eds.).
- F. Da Lio, N. Forcadel and R. Monneau,
Convergence of a non-local eikonal
equation to anisotropic mean curvature motion. Application to
dislocations dynamics , Journal of the European
Mathematical Society, 10(4), 2008, pp 1105-1119.
- A. El Hajj and N. Forcadel,
A convergent scheme for a non-local coupled system modelling
dislocations densities dynamics,
Mathematics of Computation, 77 (2008), 789-812.
- A. El Hajj,
Well-posedness theory for a non-conservative
Burger-type system arising in dislocation dynamics,
SIAM Journal on Mathematical Analysis, 39 (2007), pp. 965-986.
- A. Ghorbel , P. Hoch, R. Monneau,
A numerical study for the homogenization of one-dimensional models
describing the motion of dislocations
, Int. J. of Computing Science and Mathematics
2 (1-2) (2008), 28-52.
- C. Imbert, R. Monneau, E. Rouy,
Homogenization of first order equations with u/epsilon-periodic
Hamiltonians.
Part II: application to dislocations dynamics., accepted to
Comm. Part. Diff. Equations.
- C. Imbert and R. Monneau,
Homogenization
of first order
equations with u/epsilon-periodic
Hamiltonians. Part I: local equations, Archive for Rational
Mechanics and Analysis, 187 (1), 49-89.
- G. Barles, P. Cardaliaguet, O. Ley, R. Monneau,
General existence results and uniqueness for dislocation equations
, SIAM J. Numer. Anal. 40 (1), 44-69, (2008).
- N. Forcadel,
Dislocations dynamics with a mean curvature term: short time existence
and uniqueness, Differential
and Integral Equations, 21(3-4), pp 285-304, (2008).
- N. Forcadel, A. Monteillet,
Minimizing movements for dislocation dynamics with a mean curvature,
accepted to ESAIM: Control, Optimisation and Calculus of
Variations.
- R. Monneau,
A transport formulation of moving fronts and application to
dislocations dynamics, Interfaces and Free
Boundaries, 9, 383-409, (2007).
- E. Carlini, M. Falcone, N. Forcadel, R. Monneau,
Convergence of a Generalized Fast Marching Method for an Eikonal equation with a Velocity Changing Sign
, SIAM journal on numerical analysis,
46(6), 2008, pp. 2920-2952.
- H. Ibrahim,
Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi
coupled system describing the dynamics of dislocation densities
, Annales de l'I.H.P, Non Linear Analysis, 26 (2009) 415-435.
- N. Forcadel,
An error estimate for a new scheme for mean curvature motion
, SIAM journal on
numerical analysis, 46(5), 2008, pp. 2715-2741.
- N. Forcadel, C. Imbert, R. Monneau,
Homogenization of fully overdamped Frenkel-Kontorova
models, Journal of Differential Equations 246 (3)
(1 February 2009), 1057-1097.
- N. Forcadel, C. Imbert, R. Monneau,
Homogenization of the dislocation dynamics and of some particle systems
with two-body interaction
, Discrete and Continuous Dynamical Systems - A, vol. 23
(3) (March 2009), 785-826.
- A. El Hajj, H. Ibrahim, R. Monneau, Derivation and
study of dynamical models
of dislocation densities, ESAIM: PROCEEDINGS, 27 (2009), pp 227-239.
- H. Ibrahim, M. Jazar, R. Monneau,
Global existence of solutions to a singular parabolic/
Hamilton-Jacobi coupled system with Dirichlet conditions,
C. R. Acad. Sci. Paris, Ser. I 346 (2008) 945-950.
- N. Forcadel, R. Monneau,
Existence of solutions for a model describing the dynamics of junctions
between dislocations, accepted in SIAM J. Math. Anal.
- R. Benguria et J. Dolbeault, R. Monneau, Harnack inequalities
and discrete-continuum error estimate, accepted to J. Statistical Physics.
- N. Forcadel,
Comparison principle for a Generalized Fast Marching Method,
accepted SIAM journal on numerical analysis.
- M. Cannone, A. El Hajj, R. Monneau and F. Ribaud,
Global existence for a system of non-linear and non-local
transport equations describing the dynamics of dislocation
densities
, accepted to Archive for Rational Mechanics and
Analysis.
- N. Forcadel, C. Imbert, R. Monneau,
Viscosity solutions for particle systems and homogenization of
dislocation dynamics,
accepted to "On the notions of solutions to nonlinear elliptic problems: results and
developments".
- A. Briani, R. Monneau, Time-homogenization
of a first order system arising in the modelling of the
dynamics of dislocation densities, C. R. Acad. Sci. Paris, Ser. I 347 (2009) 231-236.
- P. Biler, G. Karch, R. Monneau, Nonlinear
diffusion of dislocation density and self-similar solutions,
accepted to Communications in Mathematical Physics.
- A. El Hajj, H. Ibrahim, R. Monneau, Homogenization of dislocation
dynamics, Materials Science and Engineering, 3 (2009) 012023.
- A. El Hajj, Short time existence and uniqueness in Hölder spaces for the
2D dynamics of dislocation densities, Annales de
l'Institut Henri Poincaré (C) Non Linear Analysis, 27 (2010) 21-35.
- A. Ghorbel and R. Monneau,
Well-posedness and numerical analysis of a
one-dimensional non-local transport equation modelling dislocations
dynamics, accepted Mathematics of Computation.
- A. El Hajj, H. Ibrahim, R. Monneau, Dislocation dynamics: from microscopic models
to macroscopic crystal plasticity, Continuum Mechanics and Thermodynamics 21 (2009), pp. 109-123.
- H. Ibrahim, M. Jazar, R. Monneau,
Dynamics of dislocation densities in a bounded channel. Part II:
existence
of weak solutions to a singular parabolic/Hamilton-Jacobi strongly
coupled system, Comm. Partial Differential Equations, 34 (8) (2009), 889-917.
- H. Ibrahim, M. Jazar, R. Monneau,
Dynamics of dislocation densities in a bounded channel.
Part I: smooth solutions to a singular coupled parabolic system
, accepted to CPAA.
- A. El Hajj, R. Monneau Global continuous solutions
for diagonal hyperbolic systems
with large and monotone data, accepted to Journal of Hyperbolic Differential Equations.
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