A quasilinear system of partial differential equations is shown to be a general model for diffusion in heterogeneous media. The system to be studied may contain very nonlinear singular or degenerate coefficients and include certain free-boundary problems that arise in various applications. The objective is to find sufficient conditions to guarantee the initial-boundary- value problem is well-posed, to investigate and compare the properties of solutions in relevant special cases, and to study the dependence of solutions on parameters or functions in the equations.
