Equivalent low-order model for a nonlinear diffusion equation

Physica D: Nonlinear Phenomena

Volumn 95, Issue 2, 1996, Pages 107-127

  Farjas, J ^a   Rosell, J I ^b   Herrero, R ^a   Pons, R ^a   Pi, F ^a   Orriols, G ^a  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

^b UNIVERSITY OF LLEIDA   (Spain)

Author keywords

Dynamical systems; Nonlinear partial differential equations

Indexed keywords

EID: 0001846324     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(96)00068-1     Document Type: Article

References (26)

1. A.A. Andronov, E.A. Vitt and S.E. Khaiken, Theory of Oscillators (Pergamon Press, Oxford, 1966).
2. J.E. Marsden and M. McCracken, The Hopf Bifurcation and Its Applications (Springer, Berlin, 1976).
3. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, New York, 1983).
4. P. Gaspard, Physica D 62 (1993) 94-122.
5. M.M. Loeve, Probability Theory (Van Nostrand, Princeton, 1955).
6. L. Sirovich, Physica D 37 (1987) 126-145.
7. P. Constantin, C. Foias, B. Nicolaenko and R. Temam, Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations (Springer, New York, 1989).
8. J.I. Rosell, J. Farjas, R. Herrero, F. Pi and G. Orriols, Physica D 85 (1995) 509-547.
9. J.I. Rosell, F. Pi, F. Boixader, R. Herrero, J. Farjas and G. Orriols, Opt. Commun. 82 (1991) 162-170.
10. R. Herrero, F. Boixader, J. Farjas, F. Pi, G. Orriols and J.I. Rosell, Opt. Commun. 113 (1994) 324-334.
11. R. Herrero, J. Farjas, R. Pons, F. Pi and G. Orriols, Phys. Rev. E, submitted.
12. M.A. Celia and W.G. Gray, Numerical Methods for Differential Equations (Prentice-Hall, Englewood Cliffs, 1992).
13. For a systematic procedure see, for example, S. Barnett and R.G. Cameron, Introduction to Mathematical Control Theory, 2nd Ed. (Clarendon Press, Oxford, 1985) 84-91.
14. J.M. Gambaudo, P. Glendinning and C. Tresser, in: Instabilities and Nonequilibrium Structures, eds. E. Tirapegui and D. Villaroel (Reidel, Dordrecht, 1987) 41-62.
15. A. Arneodo, P. Coullet and C. Tresser, J. Stat. Phys. 27 (1982) 171-182;
16. P. Gaspard, R. Krapal and G. Nicolis, J. Stat. Phys. 31 (1983) 499-518;
17. J. Stat. Phys. 35 (1984) 697-727.
18. F. Argoul, A. Arnéodo and P. Richetti, J. de Chi, Phy. 84 (1987) 1367-1385.
19. H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids (Oxford University, London, 1959) 64-70.
20. P. Coullet, C. Tresser and A. Arnéodo, Phys. Lett A 72 (1979) 268- 270;
21. A. Arnéodo, P. Coullet and E.A. Spiegel, Phys. Lett. A 92 (1982) 369-373.
22. A. Arnéodo, P. Coullet, E.A. Spiegel and C. Tresser, Physica D 14 (1985) 327-347.
23. Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 54 (1975) 687-699.
24. G. Sivashinsky, Acta Astronautica 4 (1977) 1177-1206.
25. O.E. Rössler, Phys. Lett. A 57 (1976) 397-398.
26. M. Mansuripur, G.A. Connell and J.W. Goodman, Appl. Opt. 21 (1982) 1106-1118.