𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the averaging method for rod equations with quadratic non-linearity

✍ Scribed by R. P. Buitelaar

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
867 KB
Volume
17
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The averaging method is used to approximate solutions of systems of linearly coupled, (quadratic) non‐linear dispersive wave equations, which describe extensional–torsional dynamics of a rod. Existence and uniqueness results are established. Error estimates confirm the asymptotic validity of the approximation method on a long time‐scale. The linear couplings between the equations imply that resonance can occur inside a single mode of the solution, but energy can also be transferred to other modes.

πŸ“œ SIMILAR VOLUMES

On a Galerkin-averaging method for weakl
On a Galerkin-averaging method for weakly non-linear wave equations
✍ M. S. Krol; W. Eckhaus πŸ“‚ Article πŸ“… 1989 πŸ› John Wiley and Sons 🌐 English βš– 661 KB

## Communicated by W. Eckhaus Solutions of weakly non-linear wave quations can be approximated using Galerkin's procedure combined with the averaging method. In this paper existence and uniqueness of solutions are proved in suitably chosen function spaces. Erroretimates lead us to results on asymp

Generalized Broadwell models for the dis
Generalized Broadwell models for the discrete Boltzmann equation with linear and quadratic terms
✍ Mitsuru Yamazaki πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 97 KB πŸ‘ 2 views

A generalization of the Broadwell models for the discrete Boltzmann equation with linear and quadratic terms is investigated. We prove that there exists a time-global solution to this model in one space-dimension for locally bounded initial data, using a maximum principle of solutions. The boundedne