Regularity of solutions to a dynamic frictionless contact problem with normal compliance

• Published in: Nonlinear analysis Vol. 59; no. 7; pp. 1063 - 1075
• Main Authors: Kuttler, K.L., Shillor, M.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-12-2004
• Subjects: Dynamic contact; Normal compliance; Regularity; Viscoelastic; Dynamic contact; Normal compliance; Regularity; Viscoelastic
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2004.07.049

The regularity in time of solutions to a problem of frictionless dynamic contact between a viscoelastic body and a reactive foundation is established. Contact is modeled with the normal compliance condition. It is shown that the differentiability of the normal compliance function, its behavior at the onset of contact, determines the regularity of the solution, and additional differentiability of the data and appropriate compatibility on the initial conditions yield higher solutions' differentiability. Unlike the case when the Signorini condition is used, in this problem there is no intrinsic regularity ceiling. A simple example shows that these results are close to being optimal.