a1 School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
a2 Centre d'Etudes Nucléaires, Commissariat á l'Energie Atomique, 23700 Pierrelatte, France
In the focusing problem we seek a solution to the porous medium equation whose initial distribution is in the exterior of some compact set (e.g. a ball). At a finite time T the gas will reach all points of the initially empty region R. We construct a selfsimilar solution of the radially symmetric focusing problem. This solution is an example of a selfsimilar solution of the second kind, i.e. one in which the similarity variable cannot be determined a priori from dimensional considerations. Our solution also shows that in more than one space dimension, the velocity of the gas is infinite at the centre of R at the focusing time T.
(Received May 05 1992)