Normal forms for parabolic partial differential equations

J.-P. Eckmann; H. Epstein; C. E. Wayne

Annales de l'I.H.P. Physique théorique (1993)

  • Volume: 58, Issue: 3, page 287-308
  • ISSN: 0246-0211

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Eckmann, J.-P., Epstein, H., and Wayne, C. E.. "Normal forms for parabolic partial differential equations." Annales de l'I.H.P. Physique théorique 58.3 (1993): 287-308. <http://eudml.org/doc/76607>.

@article{Eckmann1993,
author = {Eckmann, J.-P., Epstein, H., Wayne, C. E.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {normal form; resonances; partial normal form for perturbations of the Ginzburg-Landau equation; singular integral operators},
language = {eng},
number = {3},
pages = {287-308},
publisher = {Gauthier-Villars},
title = {Normal forms for parabolic partial differential equations},
url = {http://eudml.org/doc/76607},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Eckmann, J.-P.
AU - Epstein, H.
AU - Wayne, C. E.
TI - Normal forms for parabolic partial differential equations
JO - Annales de l'I.H.P. Physique théorique
PY - 1993
PB - Gauthier-Villars
VL - 58
IS - 3
SP - 287
EP - 308
LA - eng
KW - normal form; resonances; partial normal form for perturbations of the Ginzburg-Landau equation; singular integral operators
UR - http://eudml.org/doc/76607
ER -

References

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  1. [CE1] P. Collet and J.-P. Eckmann, Instabilities and Fronts in Extended Systems, Princeton University Press, 1990. Zbl0732.35074MR1109707
  2. [CE2] P. Collet and J.-P. Eckmann, The Time-dependent Amplitude Equation for the Swift-Hohenberg Problem, Commun. Math. Phys., Vol. 132, 1990, pp. 139-153. Zbl0756.35096MR1069205
  3. [D] M.Y. Denisov, Reduction of the nonlinear Diffusion Equation to linear Form, Functional Analysis and its Applications, Vol. 19, 1985, pp. 57-58. Zbl0657.34041MR783711
  4. [MS] H. Mckean and J. Shatah, The nonlinear Schrödinger Equation and the nonlinear heat Equation Reduction to normal Form, Comm. Pure Appl. Math., Vol. 44, 1991, pp. 1067-1080. Zbl0773.35075MR1127050
  5. [N] E. Nelson, Topics in Dynamics I: Flows, Princeton University Press, 1970. Zbl0197.10702MR282379
  6. [Ni] N.V. Nikolenko, Complete integrability of the nonlinear Schrödinger Equation. Soviet Math. Dokl., Vol. 17, 1976, pp. 295-298. Zbl0346.35039MR402263
  7. [PD] J. Palis and W. De Melo, Geometrical Theory of Dynamical Systems, an Introduction, Springer-Verlag, 1982. Zbl0491.58001MR669541
  8. [Se] V.I. Sedenko, On the normal Form of nonlinear partial Differential Equations on the real Axis, Math. U.S.S.R. Sbornik, Vol. 34, 1978, pp. 111-117. Zbl0403.35003MR484959
  9. [S] J. Shatah, Normal Forms and Quadratic nonlinear Klein-Gordon Equations, Comm. Pure and Appl. Math., Vol. 38, 1985, pp. 685-696. Zbl0597.35101MR803256

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