Absorbing Balls for Equations Modeling Nonuniform Deformable Bodies with Heavy Rigid Attachments
 J. Patrick Wilber
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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 infinitedimensional 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.
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 Title
 Absorbing Balls for Equations Modeling Nonuniform Deformable Bodies with Heavy Rigid Attachments
 Journal

Journal of Dynamics and Differential Equations
Volume 14, Issue 4 , pp 855887
 Cover Date
 20021001
 DOI
 10.1023/A:1020716727905
 Print ISSN
 10407294
 Online ISSN
 15729222
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 nonlinear viscoelasticity
 absorbing balls
 parabolichyperbolic equations
 Authors

 J. Patrick Wilber ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Texas A&M University, College Station, Texas, 77843