Keywords
- Periodic Solution
- Equilibrium Solution
- Simple Eigenvalue
- Floquet Multiplier
- Complex Conjugate Pair
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Bibliography
Coddington, E.A., and Levinson, N., Theory of Ordinary Differential Equations. McGraw-Hill, New York, 1955.
Frank-Kamenetzky, D.A., Diffusion and Heat Exchange in Chemical Kinetics. Princeton Univ. Press, 1955.
Gavalas, G.R., Nonlinear Differential Equations of Chemically Reacting Systems. Springer, New York, 1968.
Gelfand, I.M., "Some Problems in the Theory of Quasilinear Equations." AMS Translations Ser. 2 29, 295–381, (1963).
Hopf, E., "Abzweigung einer Periodischen Lösung eines Differential Systems." Berichten der Math.-Phys. Klasse der Sächischen Akademie der Wissenschaften zu Leipzig, XCIV, 1–22, (1942).
__, "A Mathematical Example Displaying Features of Turbulence." Comm. Pure Appl. Math., 1, 303, (1948).
Iooss, G., "Existence et Stabilité de la Solution Périodique Secondaire Intervenant dans les Problèmes d'Evolution du Type Navier Stokes." Arch. Rational Mech. Anal. 4, 47, 301–329 (1972).
Joseph, D., and Sattinger, D.H., "Bifurcating Time Periodic Solutions and Their Stability." Arch. Rational Mech. Anal. 45, 75–109 (1972).
Judovic, V.I., "On the Stability of Forced Oscillations of Fluid." Sov. Math. Dokl. 11, 1473–1477 (1970).
_____, "On the Stability of Self-Oscillations of a Liquid." Sov. Math. Dokl. 11, 1543–1546 (1970).
_____, "Appearance of Auto Oscillations in a Fluid." Prikl. Mat. Mek. 35, 638–655 (1971).
Kirchgässner, K., and Sorger, P., "Stability Analysis of Branching Solutions of the Navier-Stokes Equations." Proc. 12th Int. Cong. Appl. Mech., Stanford Univ. August, 1968.
Landau, L., "On the Problem of Turbulence." C.R. Acad. Sci. USSR 44, 311 (1944).
Lee, J.C., and Luss, D., "The Effect of Lewis Number on the Stability of a Catalytic Reaction." AIChE Journal, 16, 620–665, July, 1970.
Parks, J.R., "Criticality Criteria ... as a Function of Activation Energy and Temperature of Assembly." Jour. of Chemical Physics 34, 46–50 (1961).
Ruelle, D., and Takens, F., "On the Nature of Turbulence." Comm. Math. Phys. 20, 167–192 (1971).
Sattinger, D., "Bifurcation of Periodic Solutions of the Navier-Stokes Equations." Arch. Rational Mech. Anal. 41, 66–80 (1971).
_____, "Stability of Bifurcating Solutions by Leray-Schauder Degree." Arch. Rational Mech. Anal. 43, 154–166 (1971).
Sattinger, D., "Topics in Stability and Bifurcation Theory," Lecture Notes, University of Minnesota, to appear in the Springer Lecture Note Series.
_____, "Monotone Methods in Nonlinear Elliptic and Parabolic Boundary Value Problems." Indiana Univ. Math. Journal, 21, 979–1000 (1972).
Stuart, J.T., "On the Nonlinear Mechanics of Wave Disturbances in Stable and Unstable Parallel Flows." Jour. Fluid Mechanics 9, 353–370 (1960).
Watson, J., "On the Nonlinear Mechanics of Wave Disturbances in Stable and Unstable Parallel Flows, Part II." J. Fluid Mech. 14, 336 (1960).
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Sattinger, D.H. (1973). Six lectures on the transition to instability. In: Stakgold, I., Joseph, D.D., Sattinger, D.H. (eds) Nonlinear Problems in the Physical Sciences and Biology. Lecture Notes in Mathematics, vol 322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060571
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DOI: https://doi.org/10.1007/BFb0060571
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