  We study a system of non-identical bistable particles that is driven by a
dynamical constraint and coupled through a non-local mean-field. Assuming
piecewise affine constitutive laws we prove the existence of traveling wave
solutions and characterize their dynamical stability. Our findings explain the
two dynamical regimes for phase interface that can be observed in numerical
simulations with different parameters. We further discuss the convergence to a
rate-independent model with strong hysteresis in the limit of vanishing
relaxation time.
