  We discuss entanglement evolution of a multi-qubit system when one of its
qubits is subjected to a general noisy channel. For such a system, an evolution
equation of entanglement for a lower bound for multi-qubit concurrence is
derived. Using this evolution equation, the entanglement dynamics of an
initially mixed three-qubit state composed of a GHZ and a W state is analyzed
if one of the qubits is affected by a phase, an amplitude or a generalized
amplitude damping channel.
