Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation

Communications in Mathematical Physics

Volumn 178, Issue 3, 1996, Pages 679-702

  Schneider, Guido ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030560044     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02108820     Document Type: Article

References (30)

1. Bricmont, J., Kupiainen, A.: Renormalization group and the Ginzhurg-Landau equation. Commun. Math. Phys. 150, 193-208 (1992)
2. Bricmont, J., Kupiainen, A.: Stability of moving fronts in the Ginzburg-Landau equation. Commun. Math. Phys. 159, 287-318 (1994)
3. Collet, P., Eckmann, J.-P.: The stability of modulated fronts. Helv. Phys. Acta 60, 969-991 (1987)
4. Collet, P., Eckmann, J.-P.: Instabilities and Fronts in Extended Systems. Princeton, NJ: Princeton University Press, 1990
5. Collet, P., Eckmann, J.-P.: The time dependent amplitude equation for the Swift-Hohenberg problem. Commun. Math. Phys. 132, 139-153 (1990)
6. Collet, P., Eckmann, J.-P.: Solutions without phase-slip for the Ginsburg-Landau equation. Commun. Math. Phys. 145, 345-356 (1992)
7. Collet, P., Eckmann, J.-P., Epstein, H.: Diffusive repair for the Ginsburg-Landau equation. Helv. Phys. Acta 65, 56-92 (1992)
8. Eckhaus, W.: Studies in nonlinear stability theory. Springer tracts in Nat. Phil. Vol. 6, 1965
9. Eckhaus, W.: The Ginzburg-Landau equation is an attractor. J. Nonlinear Science 3, 329-348 (1993)
10. Eckmann, J.-P., Wayne, C.E.: The non-linear stability of front solutions for parabolic partial differential equations. Commun. Math. Phys. 161, 323-334 (1994)
11. Gallay, T.: Local stability of critical fronts in nonlinear parabolic partial differential equations. Nonlinearity 7, 741-764 (1994)
12. Gardner, R., Jones, J.K.R.T., Kapitula, T.: Stability of travelling waves for nonconvex scalar viscous conservation laws. Comm. Pure. Appl. Math. 46, 505-526 (1993)
13. Haragus, M.: The orbital stability of fronts for high order parabolic partial differential equations. In: Structure and Dynamics of Nonlinear Waves in Fluids (eds.: A. Mielke, K. Kirchgässner) World Scientific Publishing 1995, 268-274.
14. Henry, D.: Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics 840, Berlin, Heidelberg, New York: Springer, 1981
15. Kapitula, T.: On the nonlinear stability of plane waves for the Ginzburg-Landau equation. Comm. Pure. Appl. Math. 47, 831-841 (1994)
16. Kirchgässner, K.: On the nonlinear dynamics of travelling fronts. J. Diff. Eqns. 96, 256-278 (1992)
17. Kirrmann, P., Schneider, G., Mielke, A.: The validity of modulation equations for extended systems with cubic nonlinearities. Proceedings of the Royal Society of Edinburgh 122A, 85-91 (1992)
18. Mielke, A.: A new approach to sideband-instabilities using the principle of reduced instability. In: Nonlinear Dynamics and Pattern Formation in the Natural Environment (eds.: A. Doelman, A. van Harten) Longman UK 1995, 206-222
19. Mielke, A., Schneider, G.: Attractors for modulation equations on unbounded domains -Existence and comparison. Nonlinearity 8, 743-768 (1995)
20. Newell, A., Whitehead, J.: Finite bandwidth, finite amplitude convection. J. Fluid Mech. 38, 279-303 (1969)
21. Pego, R.L., Weinstein, M.I.: Asymptotic stability of solitary waves. Commun. Math. Phys. 164, 305-349 (1994)
22. Reed, M., Simon, B.: Methods of Modern Mathematical Physics 1-4. New York: Academic Press, 1972
23. Schneider, G.: A new estimate for the Ginzburg-Landau approximation on the real axis. J. Nonlinear Science 4, 23-34 (1994)
24. Schneider, G.: Error estimates for the Ginzburg-Landau approximation. J. Appl. Math. Physics (ZAMP) 45, 433-457 (1994)
25. Schneider, G.: Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations. Commun. Math. Phys. 164, 157-179 (1994)
26. Schneider, G.: Analyticity of Ginzburg-Landau modes. J. Diff. Eqns. 121, 233-257 (1995)
27. Temam, R.: Infinite-Dimensional Systems in Mechanics and Physics. Berlin, Heidelberg, New York: Springer, 1988
28. van Harten, A.: On the validity of Ginzburg-Landau's equation. J. Nonlinear Science 1, 397-422 (1991)
29. Wayne, E.C.: Invariant manifolds for parabolic partial differential equations on unbounded domains. Preprint Pennsylvania State University, 1994. To appear in Arch. Rat. Mech. 1996
30. Wayne, E.C.: Invariant manifolds for parabolic partial differential equations on unbounded domains. Preprint Pennsylvania State University, 1994. To appear in Arch. Rat. Mech. 1996