Heteroclinic Connections in the Kuramoto-Sivashinsky Equation: A Computer Assisted Proof

Reliable Computing

Volumn 3, Issue 3, 1997, Pages 277-285

  Mrozek, Marian ^a   Zelawski, Margin ^a  

^a JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041690928     PISSN: 13853139     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1009974824292     Document Type: Article

References (12)

1. Conley, Ch.: Isolated Invariant Sets and the Morse Index, CBMS Regional Conf. Ser. Math. 38, AMS, Providence, R.I., 1978.
2. Lohner, R. J.: Computation of Guaranteed Enclosures for the Solutions of Ordinary Initial and Boundary Value Problems, in: Cash, J. R. and Gladwell, I. (eds), Computational Ordinary Differential Equations, Clarendon Press, Oxford, 1992.
3. Michelson, D.: Steady Solutions of the Kuramoto-Sivashinsky Equation, Physica D 19 (1986), pp. 89-111.
4. Michelson, D. and Sivashinsky, G.: Nonlinear Analysis of Hydrodynamic Instability in Laminar Flames, II. Numerical Experiments, Acta Astronaut. 4 (1977), pp. 1207-1221.
5. Mischaikow, K. and Mrozek, M.: Chaos in Lorenz Equations: a Computer Assisted Proof, Bull. Amer. Math. Soc. (N.S.) 33 (1995), pp. 66-72.
6. Mischaikow, K. and Mrozek, M.: Chaos in Lorenz Equations: a Computer Assisted Proof, Part II: Details, Mathematics of Computation, accepted.
7. Mrozek, M.: Topological Invariants, Multivalued Maps and Computer Assisted Proofs in Dynamics, Computers and Mathematics 32 (1996), pp. 83-104.
8. Mrozek, M. and Srzednicki, R.: On Time-Duality of the Conley Index, Results in Mathematics 24 (1993), pp. 161-167.
9. Spreuer, H. and Adams, E.: On the Strange Attractor and Transverse Homoclinic Orbits for Lorenz Equations, J. Math. Anal. and Appl. 190 (1995), pp. 329-360.
10. Troy, W. C.: The Existence of Steady Solutions of the Kuramoto-Sivashinsky Equation, J. Diff. Equ. 82 (1989), pp. 269-313.
11. Zgliczynski, P.: Computer Assisted Proof of Chaos in the Hénon Map and the Rössler Equations, Nonlinearity, to appear.
12. Żelawski, M.: Rigorous Numerical Approach to Isolation in Dynamical Systems on the Example of the Kuramoto-Sivashinsky Equation, in preparation.