Computer assisted proof to symmetry-breaking bifurcation phenomena in nonlinear vibration

DOI10.1007/BF03167433zbMath1129.37338MaRDI QIDQ1880946

Tadashi Kawanago

Publication date: 27 September 2004

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Vibrations in dynamical problems in solid mechanics (74H45) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Abstract bifurcation theory involving nonlinear operators (47J15) Bifurcations in context of PDEs (35B32) Numerical bifurcation problems (65P30) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

Related Items (6)

A symmetry-breaking bifurcation theorem and some related theorems applicable to maps having unbounded derivatives ⋮ Improved convergence theorems of Newton's method designed for the numerical verification for solutions of differential equations ⋮ The Hopf bifurcation theorem in Hilbert spaces for abstract semilinear equations ⋮ Error analysis of Galerkin's method for semilinear equations ⋮ Codimension-\(m\) bifurcation theorems applicable to the numerical verification methods ⋮ Pattern formations in heat convection problems

Cites Work

• A bifurcation phenomenon for the periodic solutions of a semilinear dissipative wave equation
• A numerically based existence theorem for the Navier-Stokes equations
• Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points
• A symmetry-breaking bifurcation theorem and some related theorems applicable to maps having unbounded derivatives
• Periodic solutions to nonlinear one dimensional wave equation with 𝑋-dependent coefficients
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Computer assisted proof to symmetry-breaking bifurcation phenomena in nonlinear vibration