On the Well-posedness of Some generalized Characteristic Cauchy Problems J.-A. Marti, V. Dévoué, A. Delcroix, E. Allaud and H. Vernaeve Math. Model. Nat. Phenom., 11 2 (2016) 89-99 Published online: 21 March 2016 DOI: 10.1051/mmnp/201611207