@article{AIHPC_2009__26_2_415_0, author = {Ibrahim, Hassan}, title = {Existence and {Uniqueness} for a {Nonlinear} {Parabolic/Hamilton-Jacobi} {Coupled} {System} {Describing} the {Dynamics} of {Dislocation} {Densities}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {415--435}, publisher = {Elsevier}, volume = {26}, number = {2}, year = {2009}, doi = {10.1016/j.anihpc.2007.09.005}, mrnumber = {2504037}, zbl = {1159.74010}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2007.09.005/} }
TY - JOUR AU - Ibrahim, Hassan TI - Existence and Uniqueness for a Nonlinear Parabolic/Hamilton-Jacobi Coupled System Describing the Dynamics of Dislocation Densities JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 415 EP - 435 VL - 26 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2007.09.005/ DO - 10.1016/j.anihpc.2007.09.005 LA - en ID - AIHPC_2009__26_2_415_0 ER -
%0 Journal Article %A Ibrahim, Hassan %T Existence and Uniqueness for a Nonlinear Parabolic/Hamilton-Jacobi Coupled System Describing the Dynamics of Dislocation Densities %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 415-435 %V 26 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2007.09.005/ %R 10.1016/j.anihpc.2007.09.005 %G en %F AIHPC_2009__26_2_415_0
Ibrahim, Hassan. Existence and Uniqueness for a Nonlinear Parabolic/Hamilton-Jacobi Coupled System Describing the Dynamics of Dislocation Densities. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 2, pp. 415-435. doi : 10.1016/j.anihpc.2007.09.005. http://archive.numdam.org/articles/10.1016/j.anihpc.2007.09.005/
[1] Solutions De Viscosité Des Équations De Hamilton-Jacobi, Springer-Verlag, Paris, 1994. | MR | Zbl
,[2] Analyse Fonctionelle. Théorie Et Applications, Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris, 1983, xiv+234 pp. | MR | Zbl
,[3] M. Cannone, A. El Hajj, R. Monneau, F. Ribaud, Global existence of a system of non-linear transport equations describing the dynamics of dislocation densities, 2007, submitted for publication.
[4] Scalar Conservation Laws and Hamilton-Jacobi Equations in One Space Variables, Nonlinear Anal. 18 (5) (1992) 461-469. | MR | Zbl
,[5] Acta Materialia 54 (1997) 3164.
, , ,[6] Numerical Schemes for Conservation Laws Via Hamilton-Jacobi Equations, Math. Comp. 64 (210) (1995) 555-580, S13-S18. | MR | Zbl
, , ,[7] On Existence and Uniqueness of Solutions of Hamilton-Jacobi Equations, Nonlinear Anal. Methods Appl. 10 (4) (1986) 353-370. | MR | Zbl
, ,[8] Well-Posedness Theory for a Nonconservative Burgers-Type System Arising in Dislocation Dynamics, SIAM J. Math. Anal. 39 (3) (2007) 965-986. | MR | Zbl
,[9] A. El Hajj, N. Forcadel, A convergent scheme for a non-local coupled system modelling dislocations densities dynamics, Math. Comp. (2006), in press. | Zbl
[10] Partial Differential Equations, American Mathematical Society, Providence, RI, 1998. | MR | Zbl
,[11] Existence and Uniqueness of the Entropy Solution to a Nonlinear Hyperbolic Equation, Chin. Ann. of Math. Ser. B 16 (1) (1995) 1-14. | MR | Zbl
, , ,[12] A Note on Reservoir Simulation for Heterogeneous Porous Media, Transport Porous Media 10 (1993) 257-270.
, ,[13] Investigation of Dislocation Pattern Formation in a Two-Dimensional Self-Consistent Field Approximation, Acta Materialia 47 (1999) 3647-3654.
, ,[14] Spatial Correlations and Higher-Order Gradient Terms in a Continuum Description of Dislocation Dynamics, Acta Materialia 51 (2003) 1271-1281.
, , ,[15] Theory of Dislocations, second ed., Krieger, Malabar, FL, 1992.
, ,[16] Existence and Uniqueness of Solutions of Hamilton-Jacobi Equations, Funkcial. Ekvac. 29 (1986) 167-188. | MR | Zbl
,[17] H. Ibrahim, Rapport de recherche du CERMICS 2007-338.
[18] A Note on Front Tracking and the Equivalence Between Viscosity Solutions of Hamilton-Jacobi Equations and Entropy Solutions of Scalar Conservation Laws, Nonlinear Anal. 50 (2002) 455-469. | MR | Zbl
, ,[19] First Order Quasilinear Equations With Several Space Variables, Math. USSR Sb. 10 (1970) 217-243. | Zbl
,[20] The Cauchy Problem in the Large for Non-Linear Equations and for Certain First-Order Quasilinear Systems With Several Variables, Dokl. Akad. Nauk SSSR 155 (1964) 743-746. | MR | Zbl
,[21] Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM, Philadelphia, PA, 1973, v+48 pp. | MR | Zbl
,[22] Lower-Bound Gradient Estimates for First-Order Hamilton-Jacobi Equations and Applications to the Regularity of Propagating Fronts, Adv. Differential Equations 6 (5) (2001) 547-576. | MR | Zbl
,[23] Generalized Solutions of Hamilton-Jacobi Equations, Pitman, Boston, MA, 1982, Advanced Publishing Program. | MR | Zbl
,[24] Theory of Crystal Dislocations, Oxford, Clarendon Press, 1969.
,[25] Solutions of Hamilton-Jacobi Equations and Scalar Conservation Laws With Discontinuous Space-Time Dependence, J. Differential Equations 182 (2002) 51-77. | MR | Zbl
,[26] Linear and Nonlinear Waves, Wiley, New York, 1974. | MR | Zbl
,Cité par Sources :