If a solution of the porous medium equation initially has support in an annular domain, then the hole in the middle (bounded component of the complement of the support of the solution) will vanish in finite time. I will discuss the asymptotic behaviour of the solution when the hole fills up, first for radial solutions, and then for the nonradial case.

This is joint work with Don Aronson.

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1996-1997 Mathematics in High Performance Computing