On the large time behavior of solutions of Hamilton-Jacobi equations

SIAM Journal on Mathematical Analysis

Volumn 31, Issue 4, 2000, Pages 925-939

  Barles, G ^a   Souganidis, Panagiotis E ^b  

^a UNIVERSITÉ DE TOURS   (France)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Ergodic problem; Hamilton Jacobi equations; Hamiltonian systems; Long time behavior; Periodicity; Viscosity solutions

Indexed keywords

EID: 0034347336     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141099350869     Document Type: Article

References (10)

1. M. ARISAWA, Ergodic problem for the Hamilton-Jacobi-Bellman equation. I. Existence of the ergodic attractor, Ann. Inst. H. Poincaré Anal. Non Linéaire, 14 (1997), pp. 415-438.
2. M. ARISAWA, Ergodic problem for the Hamilton-Jacobi-Bellman equation. II, Ann. Inst. H. Poincaré Anal. Non Linéaire, 15 (1998), pp. 1-24.
3. G. BARLES, Asymptotic behavior of viscosity solutions of first-order Hamilton-Jacobi equations, Ricerche Mat., 34 (1985), pp. 227-260.
4. G. BARLES, Solutions de viscosité des équations de Hamilton-Jacobi, Math. Appl. 17, Springer-Verlag, Paris, 1994.
5. A. FATHI, Sur la convergence du semi-groupe de Lax-Oleinik, C. R. Acad. Sci. Paris Sér. I Math., 327 (1998), pp. 267-270.
6. P.-L. LIONS, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, Boston, MA, 1982.
7. P.-L. LIONS, G. PAPANICOLAOU, AND S. R. S. VARADHAN, Homogenization of Hamilton-Jacobi Equations, preprint.
8. G. NAMAH AND J. M. ROQUEJOFFRE, Remarks on the long time behavior of the solutions of Hamilton-Jacobi Equations, Comm. Partial Differential Equations, 24 (1999), pp. 883-893.
9. J. M. ROQUEJOFFRE, Comportement asymptotique des solutions d'équations de Hamilton-Jacobi monodimensionnelles, C. R. Acad. Sci. Paris Sér. I Math., 326 (1998), pp. 185-189.
10. J. M. ROQUEJOFFRE, Convergence to Steady States or Periodic Solutions in a Class of Hamilton-Jacobi Equations, preprint.