Asymptotic Behaviour of a Viscoelastic Transmission Problem with a Tip Load

Míriam S. Carneiro, Marco A. A. Fernandes, Jaime E. Muñoz Rivera


We consider a transmission problem for a string composed by two components: one ofthem is a viscoelastic material (with viscoelasticity of memory type), and the other is an elasticmaterial (without dissipation effective over this component). Additionally, we consider that in oneend is attached a tip load. The main result is that the model is exponentially stable if and only ifthe memory effect is effective over the string. When there is no memory effect, then there is a lackof exponential stability, but the tip load produces a polynomial rate of decay. That is, the tip loadis not strong enough to stabilize exponentially the system, but produces a polynomial rate of decay. 


Transmission problems; memory effect; lack of exponential stability; tip load; hybridsystem

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