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Nonlinear Dynamic Stability: A Formal Theory
57
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8
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1970
Year
EngineeringHydrodynamicsNonlinear Dynamic StabilitySystem StabilityBifurcation TheoryNonlinear MechanicsLyapunov AnalysisNon-linear MechanicsGoogle ScholarHydrodynamic StabilityStability AnalysisStability
Previous article Next article Nonlinear Dynamic Stability: A Formal TheoryBernard J. MatkowskyBernard J. Matkowskyhttps://doi.org/10.1137/0118079PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Lee A. Segel, R. J. Donnelly, , I. Prigogine and , R. Herman, Non-linear hydrodynamic stability theory and its applications to thermal convection and curved flowsNon-equilibrium Thermodynamics, Variational Techniques and Stability (Proc. Sympos. Univ. Chicago, May 17-19, 1965), Univ. Chicago Press, Chicago, Ill., 1966, 165–197 MR0214330 Google Scholar[2] Daniel D. Joseph, Nonlinear stability of the Boussinesq equations by the method of energy, Arch. Rational Mech. Anal., 22 (1966), 163–184 10.1007/BF00266474 MR0192725 0141.43803 CrossrefISIGoogle Scholar[3] P. H. Rabinowitz, Existence and nonuniqueness of rectangular solutions of the Bénard problem, Arch. Rational Mech. Anal., 29 (1968), 32–57 10.1007/BF00256457 MR0233557 0164.28704 CrossrefISIGoogle Scholar[4] W. V. R. Malkus and , G. Veronis, Finite amplitude cellular convection, J. Fluid Mech., 4 (1958), 225–260 MR0135012 0082.39603 CrossrefISIGoogle Scholar[5] J. T. Stuart, On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. I. The basic behaviour in plane Poiseuille flow, J. Fluid Mech., 9 (1960), 353–370 MR0128228 0096.21102 CrossrefISIGoogle Scholar[6] J. Watson, On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows. II, J. Fluid Mech., 9 (1960), 371–389 0096.21103 CrossrefISIGoogle Scholar[7] Wiktor Eckhaus, Studies in non-linear stability theory, Springer Tracts in Natural Philosophy, Vol. 6, Springer-Verlag New York, New York, Inc., 1965viii+117 MR0196298 0125.33101 CrossrefGoogle Scholar[8] L. Landau, On the problem of turbulence, C. R. (Doklady) Acad. Sci. URSS (N.S.), 44 (1944), 311–314 MR0011997 0063.03437 Google Scholar[9] L. D. Landau and , E. M. Lifshitz, Fluid mechanics, Translated from the Russian by J. B. Sykes and W. H. Reid. Course of Theoretical Physics, Vol. 6, Pergamon Press, London, 1959xii+536 MR0108121 Google Scholar[10] Edward L. Reiss and , Bernard J. Matkowsky, Nonlinear dynamic buckling of a compressed elastic column, Quart. Appl. Math., 29 (1971), 245–260 MR0286344 0224.73064 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Cross-diffusion effects on stationary pattern formation in the FitzHugh-Nagumo modelDiscrete and Continuous Dynamical Systems - B, Vol. 27, No. 12 Cross Ref Analysis of Spot Patterns on a Coordinate-Invariant Model for Vegetation on a Curved TerrainJ. C. Tzou and L. 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1960 | 742 | |
1958 | 651 | |
1960 | 399 | |
1944 | 320 | |
1966 | 269 | |
1968 | 152 | |
1971 | 73 | |
1966 | 24 |
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