Asymptotic analysis of some elliptic-parabolic moving boundary problems Original Research Article

We consider a radial elliptic-parabolic initial boundary value problem with flux conditions at the lateral boundary. This problem arises as a model for saturated-unsaturated flow in a porous medium. Using formal methods, we describe the nonuniform behaviour of the solutions near the extinction time, which is the time at which the unsaturated zone disappears. Borderline cases are particularly delicate and we include a physically important example in which the methods still apply. A related one-dimensional problem is also analysed, illustrating the widespread applicability of the methods used.