@article{AIHPC_2007__24_2_171_0, author = {Ghoussoub, Nassif A.}, title = {Anti-self-dual lagrangians : variational resolutions of non-self-adjoint equations and dissipative evolutions}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {24}, year = {2007}, pages = {171-205}, doi = {10.1016/j.anihpc.2006.02.002}, mrnumber = {2310692}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2007__24_2_171_0} }
Ghoussoub, Nassif. Anti-self-dual lagrangians : variational resolutions of non-self-adjoint equations and dissipative evolutions. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) pp. 171-205. doi : 10.1016/j.anihpc.2006.02.002. http://gdmltest.u-ga.fr/item/AIHPC_2007__24_2_171_0/
[1] Saddle points and existence-uniqueness for evolution equations, Differential Integral Equations 6 (1993) 1161-1171. | Zbl 0813.35026
,[2] Variational principles for operator equations and initial value problems, Nonlinear Analysis, Theory, Methods and Applications 12 (5) (1988) 531-564. | MR 940608 | Zbl 0658.47016
,[3] Optimal Control of Variational Inequalities, Research Notes in Mathematics, vol. 100, Pitman, 1984. | MR 742624 | Zbl 0574.49005
,[4] Problèmes aux limites pour les equations aux dérivées partielles du premier ordre a coefficients réels ; Théorèmes d'approximation ; Application à l'équation de transport, Ann. Sci. École Norm. Sup. (4) 3 (1970) 185-233. | Numdam | MR 274925 | Zbl 0202.36903
,[5] Y. Brenier, Order preserving vibrating strings and applications to electrodynamics and magnetohydrodynamics, Preprint, 2004. | MR 2195368 | Zbl 1107.74028
[6] Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam-London, 1973. | Zbl 0252.47055
,[7] Un principe variationnel associé à certaines equations paraboliques. Le cas independant du temps, C. R. Acad. Sci. Paris Sér. A 282 (1976) 971-974. | MR 637214 | Zbl 0332.49032
, ,[8] Un principe variationnel associé à certaines equations paraboliques. Le cas dependant du temps, C. R. Acad. Sci. Paris Sér. A 282 (1976) 1197-1198. | MR 637215 | Zbl 0334.35040
, ,[9] A variational principle for non-linear transport equations, Comm. Pure Appl. Anal. 4 (4) (2005) 735-742. | MR 2172718 | Zbl 1089.35014
,[10] N. Ghoussoub, Anti-selfdual Hamiltonians: Variational resolution for Navier-Stokes equations and other nonlinear evolutions, Comm. Pure Applied Math. (2005) 25 pp., in press.
[11] N. Ghoussoub, A class of selfdual partial differential equations and its variational principles (2005), in preparation.
[12] A least action principle for steepest descent in a non-convex landscape, Contemp. Math. 362 (2004) 177-187. | MR 2091498 | Zbl 1084.37060
, ,[13] N. Ghoussoub, A. Moameni, On the existence of Hamiltonian paths connecting Lagrangian submanifolds (2005), submitted for publication.
[14] N. Ghoussoub, A. Moameni, Selfdual variational principles for periodic solutions of Hamiltonian and other dynamical systems, Comm. Partial Differential Equations (2006), in press. | MR 2334832 | Zbl 1130.35008
[15] N. Ghoussoub, A. Moameni, Selfduality and periodic solutions of certain Schrödinger equations and infinite dimensional Hamiltonian systems (2006), in preparation.
[16] A variational principle for gradient flows, Math. Ann. 30 (3) (2004) 519-549. | MR 2099192 | Zbl 1062.35008
, ,[17] Anti-selfdual Lagrangians II: Unbounded non self-adjoint operators and evolution equations, Ann. Mat. Pura Appl. (2005) 30, pp.
, ,[18] N. Ghoussoub, L. Tzou, Iterations of anti-selfdual Lagrangians and applications to Hamiltonian systems and multiparameter gradient flows, Calc. Var. Partial Differential Equations (2006) 28 pp., in press. | MR 2235885 | Zbl 1134.49029
[19] Riemannian Geometry and Geometric Analysis, Springer University Text, 2002. | MR 1871261 | Zbl 1034.53001
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