On the uniqueness of solutions for nonlinear elliptic-parabolic equations

We prove existence, boundedness and uniqueness of solutions to Cauchy-Dirichlet problems for elliptic-parabolic systems, where the specific coupling is such that the solution of the elliptic equation forms a drift term in the parabolic equation. Such systems arise as mathematical models of various applied problems, for instance, drift-diffusion processes in semiconductors and segregation processes in alloys. Our basic assumptions are thermodynamically motivated