Abstract
A nonlinear transport problem of hyperbolic-elliptic type is studied. Using estimates of potentials over varying domains and the method of characteristics, the initial value problem for Holder continuous data can be treated as an abstract evolution equation via Picard-Lindelof theorem. In addition, a global existence result is proved. Modifications of these techniques yield shock front solutionswith smooth interfaces and an extension to the case of only bounded initial values. Moreover, long time behavior of solutions and the relation to diffeomorphisms with prescribed Jacobian determinants are analyzed.
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