"Vortex-melting front" in thin superconductors with pinning

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Magneto-optical observations of a second flux front, which occurs at the second peak in the magnetization of Bi₂ Sr₂ CaCu₂ Oₓ single crystals related to the known first order ``vortex-lattice melting'', are reconsidered. We show that, in thin samples, electrodynamics necessarily leads to an extended region in which the magnetic induction adopts a nearly constant value close to that at which the phase transition occurs at thermal equilibrium. In this region a dynamical phase mixture of vortex ``solid'' and ``liquid'' should exist. Interestingly, the observed second flux front does not mark the ``melting'' front, as it was naively interpreted earlier, but indicates the disappearance of the last ``solid droplets''.