  We consider the dynamics of particle systems where the particles are confined
by impenetrable barriers to a bounded, possibly non-convex domain $\Omega$.
When particles hit the boundary, we consider an instant change in velocity,
which turns the systems describing the particle dynamics into an ODE with
discontinuous right-hand side. Other than the typical approach to analyse such
a system by using weak solutions to ODEs with multi-valued right-hand sides
(i.e., applying the theory introduced by Filippov in 1988), we establish the
existence of mild solutions instead. This solution concept is easier to work
with than weak solutions; e.g., proving uniqueness of mild solutions is
straight-forward, and mild solutions provide a solid structure for proving
many-particle limits.
  We supplement our theory of mild solutions with an application to gradient
flows of interacting particle energies with a singular interaction potential,
and illustrate its features by means of numerical simulations on various
choices for the (non-convex) domain $\Omega$.
