| Abstract: |
| In some applications, local models may be insufficient to describe important characteristics of the phenomena under study. This may be the case when magnitudes appear in the model that can vary considerably from one area to another in close proximity, which can produce memory effects. In this work, we consider the evolutionary linear elasticity system in a thin domain, with thickness of order $\varepsilon$, and with mass density and elasticity tensor that can vary arbitrarily with $\varepsilon$. Using asymptotic techniques for thin domains and homogenization theory, we prove that when $\varepsilon$ tends to zero, a new model is obtained in the limit that can include non-local terms in time. This model has applications in biomechanics, in the study of the elastic properties of organs and tissues. |
|