Failure of convergence of the Lax-Oleinik semi-group in the time-periodic case

Bulletin de la Societe Mathematique de France

Volumn 128, Issue 3, 2000, Pages 473-483

  Fathi, Albert ^a   Mather, John N ^b  

^a UNITÉ DE MATHÉMATIQUES PURES ET APPLIQUÉES   (France)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Lagrarigian; Lax Oleinik; Semi Group

Indexed keywords

EID: 0037675095     PISSN: 00379484     EISSN: None     Source Type: Journal    
DOI: 10.24033/bsmf.2378     Document Type: Article

References (13)

1. BANCERT (V.). - Mather Sets for Twist Maps and Geodesics on Tori, Dyn. Rep., t. 1, 1988, p. 1-56.
2. BANGERT (V.). - Geodesic Rays, Busemann Functions, and Monotone Twist Maps, Calc. Var., T. 2, 1994, p. 49-63.
3. BARLES (G.), SOUGANIDIS (P.E.). - On the Large Time Behavior of Solutions of Hamilton-Jacobi Equations. - Preprint, 1998.
4. FATHI (A.). - Sur la convergence du semi-groupe de Lax-Oleinik, C. R. Acad. Sci. Paris, Série I, t. 327, 1998, p. 267-270.
5. DENZLER (J.). - Mather Sets for Plane Hamiltonian Systems, J. Applied Math. Phys. (ZAMP), t. 38, 1987, p. 791-812.
6. MAÑÉ (R.). - On the Minimizing Measures of Lagrangian Dynamical Systems, Nonlinearity, t. 5, 1992, p. 623-638.
7. MATHER (J.). - Differentiability of the Minimal Average Action as a Function of the Rotation Number, Bol. Soc. Bras. Mat., t. 21, 1990, p. 59-70.
8. MATHER (J.). - Action Minimizing Measures for Positive Definite Lagrangian Systems, Math. Z., t. 207, 1991, p. 169-207.
9. MATHER (J.). - Variational Construction of Connecting Orbits, Arm. Inst. Fourier, Grenoble, t. 43, 1993, p. 1349-1386.
10. NAMAH. (G.), ROQUEJOFFRE, (J.-M.). - Comportement asymptotique des solutions d'une classe d'équations paraboliques et de Hamilton-Jacobi, C. R. Acad. Sci. Paris, Série I, t. 324, 1997, p. 1367-1370.
11. NAMAH. (G.), ROQUEJOFFRE, (J.-M.). - Remarks on the Long Time Behavior of the Solutions of Hamilton-Jacobi Equations, Comm. Partial Diff. Eq., t. 5, 1999, p. 883-894..
12. ROQUEJOFFRE (J.-M.). - Comportement asymptotique des solutions d'équations de Hamilton-Jacobi monodimensionnelles, C. R. Acad. Sci. Paris, Série I, t. 326, 1998, p. 185-189.
13. ROQUEJOFFRE (J.-M.). - Convergence to Steady States or Periodic Solutions in a Class of Hamilton-Jacohi Equations. - Preprint, 1998.