We question here the uniqueness of the D(k) relation for overdriven detonations (or for negative curvature). To this end we run a 2D hydrocode with a reactive flow model for overdriven detonations in a rod. We force the overdriven detonation by applying a travelling wave boundary condition at the radial boundary. We change separately the travelling wave velocity (D), which is also the steady detonation velocity in the rod, and the initial boundary pressure P_0. From each run we obtain the value of the negative curvature on the axis, and we plot the pairs (D,k_0) on the (D,k) plane. From the results we conclude that there is no unique D(k) relation in the negative curvature range.
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