  Levy walks (LWs) define a fundamental class of finite velocity stochastic
processes that can be introduced as a special case of continuous time random
walks. Alternatively, there is a hyperbolic representation of them in terms of
partial probability density waves. Using the latter framework we explore the
impact of aging on LWs, which can be viewed as a specific initial preparation
of the particle ensemble with respect to an age distribution. We show that the
hyperbolic age formulation is suitable for a simple integral representation in
terms of linear Volterra equations for any initial preparation. On this basis
relaxation properties and first passage time statistics in bounded domains are
studied by connecting the latter problem with solute release kinetics. We find
that even normal diffusive LWs may display anomalous relaxation properties such
as stretched exponential decay. We then discuss the impact of aging on the
first passage time statistics of LWs by developing the corresponding Volterra
integral representation. As a further natural generalization the concept of LWs
with wearing is introduced to account for mobility losses.
