  Progress of silicon based technology is nearing its physical limit, as
minimum feature size of components is reaching a mere 10 nm. The resistive
switching behaviour of transition metal oxides and the associated memristor
device is emerging as a competitive technology for next generation electronics.
Significant progress has already been made in the past decade and devices are
beginning to hit the market; however, it has been mainly the result of
empirical trial and error. Hence, gaining theoretical insight is of essence. In
the present work we report the striking result of a connection between the
resistive switching and {\em shock wave} formation, a classic topic of
non-linear dynamics. We argue that the profile of oxygen vacancies that migrate
during the commutation forms a shock wave that propagates through a highly
resistive region of the device. We validate the scenario by means of model
simulations and experiments in a manganese-oxide based memristor device. The
shock wave scenario brings unprecedented physical insight and enables to
rationalize the process of oxygen-vacancy-driven resistive change with direct
implications for a key technological aspect -- the commutation speed.
