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We study a system of non-identical bistable particles that is driven by adynamical constraint and coupled through a non-local mean-field. Assumingpiecewise affine constitutive laws we prove the existence of traveling wavesolutions and characterize their dynamical stability. Our findings explain thetwo dynamical regimes for phase interface that can be observed in numericalsimulations with different parameters. We further discuss the convergence to arate-independent model with strong hysteresis in the limit of vanishingrelaxation time.

Instability of hysteretic phase interfaces in a mean-field model with inhomogeneities