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

Albert Fathi; John Mather

Bulletin de la Société Mathématique de France (2000)

  • Volume: 128, Issue: 3, page 473-483
  • ISSN: 0037-9484

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Fathi, Albert, and Mather, John. "Failure of convergence of the Lax-Oleinik semi-group in the time periodic case." Bulletin de la Société Mathématique de France 128.3 (2000): 473-483. <http://eudml.org/doc/87836>.

@article{Fathi2000,
author = {Fathi, Albert, Mather, John},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Lagrangian; Lax-Oleinik semigroup},
language = {eng},
number = {3},
pages = {473-483},
publisher = {Société mathématique de France},
title = {Failure of convergence of the Lax-Oleinik semi-group in the time periodic case},
url = {http://eudml.org/doc/87836},
volume = {128},
year = {2000},
}

TY - JOUR
AU - Fathi, Albert
AU - Mather, John
TI - Failure of convergence of the Lax-Oleinik semi-group in the time periodic case
JO - Bulletin de la Société Mathématique de France
PY - 2000
PB - Société mathématique de France
VL - 128
IS - 3
SP - 473
EP - 483
LA - eng
KW - Lagrangian; Lax-Oleinik semigroup
UR - http://eudml.org/doc/87836
ER -

References

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  2. [2] BANGERT (V.). — Geodesic Rays, Busemann Functions, and Monotone Twist Maps, Calc. Var., t. 2, 1994, p. 49-63. Zbl0794.58010MR97b:53041
  3. [3] BARLES (G.), SOUGANIDIS (P.E.). — On the Large Time Behavior of Solutions of Hamilton-Jacobi Equations. — Preprint, 1998. 
  4. [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. Zbl1052.37514MR2000a:37058
  5. [5] DENZLER (J.). — Mather Sets for Plane Hamiltonian Systems, J. Applied Math. Phys. (ZAMP), t. 38, 1987, p. 791-812. Zbl0641.70014MR89h:58055
  6. [6] MAà'É (R.). — On the Minimizing Measures of Lagrangian Dynamical Systems, Nonlinearity, t. 5, 1992, p. 623-638. Zbl0799.58030MR93h:58059
  7. [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. Zbl0766.58033MR92j:58061
  8. [8] MATHER (J.). — Action Minimizing Measures for Positive Definite Lagrangian Systems, Math. Z., t. 207, 1991, p. 169-207. Zbl0696.58027MR92m:58048
  9. [9] MATHER (J.). — Variational Construction of Connecting Orbits, Ann. Inst. Fourier, Grenoble, t. 43, 1993, p. 1349-1386. Zbl0803.58019MR95c:58075
  10. [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. Zbl0878.35056MR98c:35078
  11. [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. Zbl0924.35028MR2000j:35034
  12. [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. Zbl0924.70017MR1646936
  13. [13] ROQUEJOFFRE (J.-M.). — Convergence to Steady States or Periodic Solutions in a Class of Hamilton-Jacobi Equations. — Preprint, 1998. 

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