We study a nonlinear elliptic-parabolic PDE in one-dimensional space with the form: b(u)t−a(u,φ(u)x)x=f. Using the nonlinear semigroups theory in Banach spaces, we establish existence and uniqueness of mild solutions of the associated Cauchy problem under general assumptions on the data. We prove under additional assumptions, that mild solutions are entropy solutions.

one space dimension; nonlinear semigroups; mild solutions