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An Elastic Contact Problem with Normal Compliance and Memory Term

Barboteu M., Ramadan A., Sofonea M. T., Patrulescu F.

Machine Dynamics Research

2012

Vol. 36, No. 1

24-34

We consider a history-dependent problem which describes the contact between an elastic body and an obstacle, the so-called foundation. The contact is frictionless and is modeled with a version of the normal compliance condition in which the memory effects are taken into account. The mathematical analysis of the problem, including existence, uniqueness and convergence results, was provided in (Barboteu et al., in preparation). Here we present the analytic expression of the solution and numerical simulations, in the study of one and two-dimensional examples, respectively.

Exponential stability and blow up for a problem with Balakrishnan-Taylor damping

Tatar N.-E., Zaraï A.

Demonstratio Mathematica

2011

Vol. 44, nr 1

67-90

This work is devoted to the study of a nonlinear viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping. We show that the weak dissipation producedby the memory term is strong enough to stabilize solutions exponentially. Also, we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a stronger damping.