Limiting profiles in contaminant transport through porous media

The degenerate nonlinear diffusion problem Beta (u) sub t + u sub x = u sub xx t 0, x between minus and positive infinity, u(x,0) = u sub 0 (x) is investigated. For a special choice of Beta (Beta (u) = u sup p, p 0) the equation describes the one-dimensional transport of contaminant in a fluid flow through a homogeneous staturated porous medium. The large time behavior of the solution is studied for more general Beta. Depending upon the shape of Beta (convex or concave) and the values u0 (- inf) and u0 (+ inf) the solution converges to a traveling wave g of the form g(x-at) or to a function w* of the form w* (x/t+1).