Computer assisted proof to symmetry-breaking bifurcation phenomena in nonlinear vibration
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- Kawanago, T. Japan J. Indust. Appl. Math. (2004) 21: 75. doi:10.1007/BF03167433
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Using the numerical verification method, we analyze a nonlinear vibration system with friction described by a wave equation related to the Duffing equation. We present a complete proof of the existence of a symmetry-breaking bifurcation point, which was first found in the numerical simulation. Our method is based on some general theorems established by the author in another paper  and is applicable to various systems described by semilinear partial differential equations including elliptic and parabolic ones. All of the numerical results in the proof can be accurately reproduced, though some of them are comparatively large scale. This reproducibility is realized by introducing a method for completely controlling the numerical calculations.