Well-posedness for a scalar conservation law with singular nonconservative source

We consider the Cauchy problem for the 2 x 2 strictly hyperbolic system [GRAPHICS] For possibly large, discontinuous data, the continuous dependence of the solution with respect to both a(0) and u(0) is shown. Moreover, the solutions are characterized as unique limits of Kruzkov's entropic solutions constructed with regularized initial data a(0)(epsilon). (C) 2004 Elsevier Inc. All rights reserved.