Kamaev, D. A. Hopf’s conjecture for a class of chemical kinetics equations. (English) Zbl 0531.35040 J. Sov. Math. 25, 836-849 (1984). Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 110, 57-73 (Russian) (1981; Zbl 0484.35043). Cited in 5 Documents MSC: 35G10 Initial value problems for linear higher-order PDEs 35K25 Higher-order parabolic equations 37-XX Dynamical systems and ergodic theory 35P20 Asymptotic distributions of eigenvalues in context of PDEs 80A30 Chemical kinetics in thermodynamics and heat transfer 35K55 Nonlinear parabolic equations Keywords:Hopf’s conjecture; chemical kinetics equations; quasilinear parabolic systems; linear principal part; attractors; dynamic systems; Dirichlet condition; Neumann condition Citations:Zbl 0484.35043 PDF BibTeX XML Cite \textit{D. A. Kamaev}, J. Sov. Math. 25, 836--849 (1984; Zbl 0531.35040) Full Text: DOI OpenURL References: [1] G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems, Wiley, New York (1977). [2] O. A. Ladyzhenskaya, Boundary Value Problems of Mathematical Physics, Plenum Publ. (1971). · Zbl 0169.00206 [3] O. A. Ladyzhenskaya, Mathematical Theory of Viscous Imcompressible Flow, Gordan and Breach (1969). · Zbl 0184.52603 [4] Q. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968). [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). [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). [7] O. A. Ladyzhenskaya and V. A. Solonnikov, On the Linearization Principle and Invariant Manifolds for Magnetohydrodynamics Problems, Dilizhen (1974). · Zbl 0404.35089 [8] R. Mane, ”Reduction of semilinear parabolic equations to finite-dimensional C1-flows,” Lect. Notes Math.,597, 361–378 (1977). [9] D. A. Kamaev, ”Hyperbolic limit sets of evolution equations and the Galerkin method,” Usp. Mat. Nauk,35, No. 3, 188–192 (1980). · Zbl 0461.35011 [10] J. E. Marsden and M. McCracken, The Hopf Bifurcation and Its Applications, Springer-Verlag, New York (1976). · Zbl 0346.58007 [11] M. Hirsch, C. Pugh, and M. Shub, ”Invariant manifolds,” Preprint (1969). · Zbl 0355.58009 [12] A. G. Postnikov, Introduction to the Analytic Theory of Numbers [in Russian], Nauka, Moscow (1971). · Zbl 0231.10001 [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). · JFM 39.0264.03 [14] L. J. Risman, ”A new proof of the three squares theorem,” J. Number Theory,6, No. 4, 282–283 (1974). · Zbl 0285.10036 [15] E. Hopf, ”A mathematical example displaying features of turbulence,” Commun. Pure Appl. Math.,1, 303–322 (1948). · Zbl 0031.32901 [16] R. F. Williams, ”One dimensional nonwandering sets,” Topology,6, 473–478 (1967). · Zbl 0159.53702 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.