On the quasistatic limit of some dynamical problems with dissipative terms

This thesis is devoted to the analysis of the asymptotic behaviour of two damped dynamical problems as inertia vanishes. Thanks to the presence of dissipative terms, we prove that in both cases the limit evolution is quasistatic and rate-independent; the role of the damping is crucial for the validity of the result, since counterexamples in the dissipation-free setting are known. Our main contribution is thus the confirmation for the two considered models of the tendency of dynamical systems to be close to their quasistatic counterpart (when inertia is small) only if suitable dissipation mechanisms are taken into account. Their presence is indeed necessary to erase in the limit all the kinetic effects, which otherwise survive and can not be detected by a pure quasistatic analysis.