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Computer assisted proof to symmetry-breaking bifurcation phenomena in nonlinear vibration. (English) Zbl 1129.37338
See the review of the preceding paper by the author [ibid. 57–74 (2004; Zbl 1054.37030)].
37G40Symmetries, equivariant bifurcation theory
47J15Abstract bifurcation theory
34C15Nonlinear oscillations, coupled oscillators (ODE)
34C23Bifurcation (ODE)
35B32Bifurcation (PDE)
58E07Abstract bifurcation theory
65P30Bifurcation problems (numerical analysis)
74H45Vibrations (dynamical problems in solid mechanics)
[1]V. Barbu and N.H. Pavel, Periodic solutions to nonlinear one dimensional wave equation with X-dependent coefficients. Trans. Amer. Math. Soc.,349 (1997), 2035–2048. · Zbl 0880.35073 · doi:10.1090/S0002-9947-97-01714-5
[2]J.G. Heywood, W. Nagata and W. Xie, A numerically based existence theorem for the Navier-Stokes equations. J. Math. Fluid. Mech.,1 (1999), 5–23. · Zbl 0934.35115 · doi:10.1007/s000210050002
[3]T. Kawanago, A symmetry-breaking bifurcation theorem and some related theorems applicable to maps having unbounded derivatives. Japan J. Indust. Appl. Math.,21 (2004), 57–74. · Zbl 1054.37030 · doi:10.1007/BF03167432
[4]T. Kawanago, Analysis for bifurcation phenomena of nonlinear vibrations. Numerical Solution of Partial Differential Equations and Related Topics II, RIMS Kokyuroku1198 (2001), 13–20.
[5]T. Kawanago, Applications of computer algebra to some bifurcation problems in nonlinear vibrations. Computer Algebra – Algorithms, Implementations and Applications, RIMS Kokyuroku1295 (2002), 137–143.
[6]T. Kawanago, Approximation of linear differential operators by almost diagonal operators and its applications. Preprint.
[7]Y. Komatsu, A bifurcation phenomenon for the periodic solutions of a semilinear dissipative wave equation. J. Math. Kyoto Univ.,41 (2001), 669–692.
[8]O.A. Ladyzenskaja, V.A. Solonnikov and N.N. Ural’ceva, Linear and Quasilinear Equations of Parabolic Type. American Mathematical Society, 1968.
[9]A. Matsumura, Bifurcation phenomena for the Duffing equation. Advances in Nonlinear Partial Differential Equations and Stochastics (eds. Kawashima and Yanagisawa), World Scientific, 1998.
[10]S. Oishi, Introduction to Nonlinear Analysis (in Japanese). Corona-sha, 1997.
[11]T. Nishida, Y. Teramoto and H. Yoshihara, Bifurcation problems for equations of fluid dynamics and computer aided proof. Lecture Notes in Numer. Appl. Anal.14, Springer, 1995, 145–157.
[12]M. Plum, Enclosures for two-point boundary value problems near bifurcation points. Scientific Computing and Validated Numerics (Wuppertal, 1995), Math. Res.90, Akademie Verlag, Berlin, 1996, 265–279.
[13]T. Tsuchiya, Numerical verification of simple bifurcation points. RIMS Kokyuroku831 (1993), 129–140.
[14]T. Tsuchiya and M.T. Nakao, Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points. Japan J. Indust. Appl. Math.,14 (1997), 357–372. · Zbl 0890.34013 · doi:10.1007/BF03167389