F. Bouchut et F. James, ONE-DIMENSIONAL TRANSPORT-EQUATIONS WITH DISCONTINUOUS COEFFICIENTS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 320(9), 1995, pp. 1097-1102
We give two formulations for transport equations with discontinuous co
efficients, which lead to existence and uniqueness for the Cauchy prob
lem, and to weak stability results.