Global attractors for degenerate partial differential equations from nonlinear viscoelasticity
- 作者：Wilber ; J. Patrick ; Antman ; Stuart S.
- 关键词：83.50.Gd ; 02.30.Jr ; 83.10.Dd ; Global attractors ; Viscoelasticity ; Hyperbolic&ndash ; parabolic equations
- 刊名：Physica D
- 出版年：2001
- 期刊代码：55_01672789
- 类别：ph
- 出版时间：April 1, 2001
- 卷：150
- 期：3-4
- 页码：177-206
- 文件大小：376 K
摘要
We study several problems for the forced motion of light, uniform, nonlinearly viscoelastic bodies carrying heavy attachments. A ‘reduced’ problem for such motions is obtained by setting the ratio of the inertia of the viscoelastic body to the inertia of the attachment equal to zero. Using methods from infinite-dimensional dynamical systems theory, we prove that the degenerate partial differential equation of this reduced problem has an attractor and that this attractor is contained in an invariant two-dimensional manifold on which solutions are governed by the classical ordinary differential equation for the forced motion of a particle on a massless spring.