1. Gas transport in a porous medium The evolution of the density u of a gas flowing trough a porous medium can be described by the so called porous medium equation: for m > 1, (1) du - Au" = 0. For space dimensiond in the domain R" x (0, ox) the equation has a radially symmetrict exact solution, the so-called Barenblatt solution: b(x, t) a(m - 1)r2 2dmt (2) = max 0, t"" Here, r= r| and a= This solution has finite support and spreads a finite amount of mass over the space domain.