On voit done que la condition nécessaire pour que les séries (2) puissent représenter les intégrales générales du système d'équations différentielles (1), n'est remplie que si les constantes$A, B, C, x$_{0},$y$_{0},$z$_{0}satisfont à l'une des quatre conditions suivantes:(1) $$A = B = C,$$ (2) $$x_0 = y_0 = z_0 = o,$$ (3) $$A = B, x_0 = y_0 = o,$$ (4) $$A = B = 2C, z_0 = o.$$

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In this paper, we study a time-domain spherical cloaking model recently introduced by Zhao and Hao (2009). This model is quite complicated and is composed of four coupled differential equations. Here we first prove the existence and uniqueness of a solution for this model. Then we obtain a stability result, which analysis is quite involved due to the coupling between the four variables. To our best knowledge, this is the first well-posedness study carried out for the time-domain cloaking model with metamaterials.