Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

A Nekhoroshev type theorem for the nonlinear Klein-Gordon equation with potential
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doi:10.3934/dcdsb.2017215      Abstract        References        Full text (488.0K)      

Stefano Pasquali - Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy (email)

1 D. Bambusi, Nekhoroshev theorem for small amplitude solutions in nonlinear Schrödinger equations, Mathematische Zeitschrift, 230 (1999), 345-387.       
2 D. Bambusi, On long time stability in Hamiltonian perturbations of non-resonant linear PDEs, Nonlinearity, 12 (1999), 823-850.       
3 D. Bambusi, Birkhoff normal form for some nonlinear PDEs, Communications in Mathematical Physics, 234 (2003), 253-285.
4 D. Bambusi, J.-M. Delort, B. Grébert and J. Szeftel, Almost global existence for Hamiltonian semilinear Klein-Gordon equations with small Cauchy data on Zoll manifolds, Communications on Pure and Applied Mathematics, 60 (2007), 1665-1690.       
5 D. Bambusi and B. Grébert, Birkhoff normal form for partial differential equations with tame modulus, Duke Mathematical Journal, 135 (2006), 507-567.       
6 D. Bambusi and N. N. Nekhoroshev, A property of exponential stability in nonlinear wave equations near the fundamental linear mode, Physica D: Nonlinear Phenomena, 122 (1998), 73-104.       
7 D. Bambusi and N. N. Nekhoroshev, Long time stability in perturbations of completely resonant PDE's, Acta Applicandae Mathematica, 70 (2002), 1-22.       
8 G. Benettin, L. Galgani and A. Giorgilli, A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems, Celestial Mechanics and Dynamical Astronomy, 37 (1985), 1-25.
9 J.-M. Delort, On long time existence for small solutions of semi-linear Klein-Gordon equations on the torus, Journal d'Analyse Mathématique, 107 (2009), 161-194.       
10 J.-M. Delort and R. Imekraz, Long time existence for the semi-linear Klein-Gordon equation on a compact boundaryless Riemannian manifold, Communications in Partial Differential Equations, 42 (2017), 388-416.       
11 J.-M. Delort and J. Szeftel, Long-time existence for small data nonlinear Klein-Gordon equations on tori and spheres, International Mathematics Research Notices, 37 (2004), 1897-1966.       
12 D. Fang, Z. Han and Q. Zhang, Almost global existence for the semi-linear Klein-Gordon equation on the circle, Journal of Differential Equations, 262 (2017), 4610-4634.       
13 D. Fang and Q. Zhang, Long-time existence for semi-linear Klein-Gordon equations on tori, Journal of Differential Equations, 249 (2010), 151-179.       
14 E. Faou and B. Grébert, A Nekhoroshev-type theorem for the nonlinear Schrödinger equation on the torus, Analysis & PDE, 6 (2013), 1243-1262.       
15 E. Faou, B. Grébert and E. Paturel, Birkhoff normal form for splitting methods applied to semilinear Hamiltonian PDEs. Part II. Abstract splitting, Numerische Mathematik, 114 (2010), 459-490.       
16 P. Lochak, Canonical perturbation theory via simultaneous approximation, Russian Mathematical Surveys, 47 (1992), 57-133.       
17 K. Nakanishi and W. Schlag, Invariant Manifolds and Dispersive Hamiltonian Evolution Equations, European Mathematical Society, 2011.       
18 N. N. Nekhoroshev, An exponential estimate of the time of stability of nearly-integrable Hamiltonian systems, (Russian)Uspehi Mat. Nauk, 32 (1977), 5-66.       
19 S. Pasquali, Long time behaviour of the nonlinear Klein-Gordon equation in the nonrelativistic limit, II, preprint, arXiv:1703.01618.
20 J. Pöschel, Nekhoroshev estimates for quasi-convex Hamiltonian systems, Mathematische Zeitschrift, 213 (1993), 187-216.       
21 J. Pöschel, On Nekhoroshev estimates for a nonlinear Schrödinger equation and a theorem by Bambusi, Nonlinearity, 12 (1999), 1587-1600.       
22 H. Rüssmann, Invariant tori in non-degenerate nearly integrable Hamiltonian systems, Regular and Chaotic Dynamics, 6 (2001), 119-204.       

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