Journal of Dynamics and Differential Equations

, Volume 14, Issue 4, pp 855–887

Absorbing Balls for Equations Modeling Nonuniform Deformable Bodies with Heavy Rigid Attachments

  • J. Patrick Wilber

DOI: 10.1023/A:1020716727905

Cite this article as:
Wilber, J.P. Journal of Dynamics and Differential Equations (2002) 14: 855. doi:10.1023/A:1020716727905


We study degenerate nonlinear partial differential equations with dynamical boundary conditions describing the forced motions of nonuniform deformable bodies with heavy rigid attachments. We prove that the dynamical system generated by a discretization of these equations has an absorbing ball whose size is independent of the order of the discretization. This result implies the existence of an absorbing ball for the infinite-dimensional dynamical system corresponding to the original degenerate partial differential equation and thereby serves as a critical step for establishing the existence of global attractors for this system. Our results also address the interesting mechanical question of how nonuniformity complicates the longterm dynamics of the coupled systems we consider.

nonlinear viscoelasticityabsorbing ballsparabolic-hyperbolic equations

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • J. Patrick Wilber
    • 1
  1. 1.Department of MathematicsTexas A&M UniversityCollege Station