Journal of Soviet Mathematics

, Volume 25, Issue 1, pp 836–849 | Cite as

Hopf's conjecture for a class of chemical kinetics equations

  • D. A. Kamaev
Article

Abstract

For quasilinear parabolic systems with a linear principal part, one investigates the question of the validity of Hopf's conjecture, concerning attractors.

Keywords

Kinetics Equation Chemical Kinetics Parabolic System Principal Part Quasilinear Parabolic System 

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Literature cited

  1. 1.
    G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems, Wiley, New York (1977).Google Scholar
  2. 2.
    O. A. Ladyzhenskaya, Boundary Value Problems of Mathematical Physics, Plenum Publ. (1971).Google Scholar
  3. 3.
    O. A. Ladyzhenskaya, Mathematical Theory of Viscous Imcompressible Flow, Gordan and Breach (1969).Google Scholar
  4. 4.
    Q. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968).Google Scholar
  5. 5.
    O. A. Ladyzhenskaya (Ladyzenskaja), V. A. Solonnikov, and N. N. Ural'tseva (Ural'ceva), Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence (1968).Google Scholar
  6. 6.
    O. A. Ladyzhenskaya, “On the dynamical system, generated by the Navier-Stokes equations,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,27, 91–114 (1972).Google Scholar
  7. 7.
    O. A. Ladyzhenskaya and V. A. Solonnikov, On the Linearization Principle and Invariant Manifolds for Magnetohydrodynamics Problems, Dilizhen (1974).Google Scholar
  8. 8.
    R. Mane, “Reduction of semilinear parabolic equations to finite-dimensional C1-flows,” Lect. Notes Math.,597, 361–378 (1977).Google Scholar
  9. 9.
    D. A. Kamaev, “Hyperbolic limit sets of evolution equations and the Galerkin method,” Usp. Mat. Nauk,35, No. 3, 188–192 (1980).Google Scholar
  10. 10.
    J. E. Marsden and M. McCracken, The Hopf Bifurcation and Its Applications, Springer-Verlag, New York (1976).Google Scholar
  11. 11.
    M. Hirsch, C. Pugh, and M. Shub, “Invariant manifolds,” Preprint (1969).Google Scholar
  12. 12.
    A. G. Postnikov, Introduction to the Analytic Theory of Numbers [in Russian], Nauka, Moscow (1971).Google Scholar
  13. 13.
    E. Landau, “Über die Einteilung der positiven Zahlen nach vier Klassen nach der Mindestzahl der zu ihrer addition Zusammensetzung erforderlichen Quadrate,” Arch. Math. Phys.,3, Reihe 13, No. 4, 305–312 (1908).Google Scholar
  14. 14.
    L. J. Risman, “A new proof of the three squares theorem,” J. Number Theory,6, No. 4, 282–283 (1974).Google Scholar
  15. 15.
    E. Hopf, “A mathematical example displaying features of turbulence,” Commun. Pure Appl. Math.,1, 303–322 (1948).Google Scholar
  16. 16.
    R. F. Williams, “One dimensional nonwandering sets,” Topology,6, 473–478 (1967).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • D. A. Kamaev

There are no affiliations available

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