Abstract:
In this talk, we present some progress on a model related to the open
problem of dynamic fracture. We study a simplified, one-dimensional
model that still presents the main difficulties of the general
problem, such as the coupling of the wave equation in a time-dependent
domain with Griffith's criterion, which states how this domain
evolves. We prove existence and uniqueness of the dynamic evolutions
for the coupled problem and then we focus on the quasistatic limit as
the speed of loading tends to zero. We shall find that this limit
evolution is not, in general, an equilibrium since it does not satisfy
Griffith's criterion in its quasistatic version.