Limiting profiles in contaminant transport through porous media

In this paper the following degenerate nonlinear diffusion problem is investigated: β(μ)/sub t/+u/sub x/=μ/sub xx/, t>0, -∞0) the equation describes the one-dimensional transport of contaminant in a fluid flow through a homogeneous saturated porous medium. Here the large time behaviour of the solution of the above problem is studied for more general β. It turns out that, depending upon the shape of β (convex or concave) and the values μ/sub o/(-∞) and μ/sub o/(+∞), the solution converges to a travelling wave g of the form g(x-at) or to a function ω* of the form ω*(x/