Sala Seminari (Dip. Matematica).
We present a simplified model of dynamic crack propagation, where the equation of elastodynamics is coupled with Griffith’s principle. In recent years there has been an increasing interest in studying systems where second-order equations for displacements are coupled with first-order flow rules for internal variables. Despite a number of papers devoted to regularised models, only partial results are available for dynamic fracture and heavy mathematical difficulties have to be overcome. In our work we deal with a problem of debonding propagation for a one-dimensional thin film, partially glued on a substrate and subject to oscillations in the debonded part. We provide existence and uniqueness results for dynamic evolutions and study the limit as the speed of external loading tends to zero. We establish the properties of the limit solution and see that in general it does not coincide with the expected quasistatic limit. Joint collaboration with Gianni Dal Maso and Lorenzo Nardini (SISSA).