Initial-boundary value problems for nearly incompressible vector fields,   and applications to the Keyfitz and Kranzer system
  We establish existence and uniqueness results for initial boundary value problems with nearly incompressible vector fields. We then apply our results to establish well-posedness of the initial-boundary value problem for the Keyfitz and Kranzer system of conservation laws in several space dimensions. 
Anupam Pal Choudhury, Gianluca Crippa, Laura V. Spinolo
math.AP