Pseudotrajectories generated by a discretization of a parabolic equation

Journal of Dynamics and Differential Equations

Volumn 8, Issue 2, 1996, Pages 281-297

  Eirola, Timo ^a   Pilyugin, Sergei Yu ^b  

^a AALTO UNIVERSITY   (Finland)

^b ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

Attractors; Parabolic equations; Pseudotrajectories

Indexed keywords

EID: 0040760978     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1007/BF02218893     Document Type: Article

References (17)

1. Angenent, S. B. (1986). The Morse-Smale property for a semi-linear parabolic equation. J. Diff. Eq. 62, 427-442.
2. Babin, A. V., and Vishik, M. I. (1992). Attractors of Evolution Equations, Stud. Math. Appl. 25, North-Holland, Amsterdam.
3. Brunovsky, P., and Chow, S.-N. (1984). Generic properties of stationary state solutions of reaction-diffusion equations. J. Diff. Eq. 53, 1-23.
4. Conley, C. (1978). Isolated Invariant Sets and the Morse Index, Region. Conf. Ser. Math. 38, AMS.
5. Douady, A., and Oesterlé, J. (1980). Dimension de Hausdorff des attracteurs. C.R. Acad. Sci. 290, 1135-1138.
6. Hale, J. K. (1988). Asymptotic Behavior of Dissipative Systems, Math. Surv. Monogr. 25, AMS.
7. Hale, J. K. (1994). Numerical dynamics. In Kloeden, P., and Palmer, K. (eds.), Chaotic Numerics, Contemp. Math. 172.
8. Henry, D. B. (1985). Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations. J. Diff. Eq. 59, 165-205.
9. Hirsch, M. W. (1976). Differential Topology, Springer-Verlag, New York.
10. Humphries, A. R., Jones, D. A., and Stuart, A. M. (1993). Approximation of dissipative partial differential equations over long time intervals. In Griffits, D. F., and Watson, G. A. (eds.), Numerical Analysis, Proc. 1993 Dundee Num. Anal. Conf.
11. Ladyzhenskaya, O. A. (1991a). Attractors for Semi-Groups and Evolution Equations, Cambridge University Press, Cambridge.
12. Ladyzhenskaya, O. A. (1991b). Globally Stable Difference Schemes and Their Attractors, Preprint POMI P-5-91, St. Petersburg.
13. Levinson, N. (1944). Transformation theory of non-linear equations of the second order. Ann. Math. 45.
14. n with oscillatory Jacobians. Publ. Mat. (in press).
15. Pilyugin, S. Yu. (1992). Introduction to Structurally Stable Systems of Differential Equations, Birkhäuser, Basel.
16. Pilyugin, S. Yu. (1994a). Complete families of pseudotrajectories and shape of attractors. Rand. Comp. Dyn. 2, 205-226.
17. 0-Topology, LN Math. 1571, Springer-Verlag, Berlin-Heidelberg.