THE FOCUSING PROBLEM FOR THE RADIALLY SYMMETRICAL POROUS-MEDIUM EQUATION

In the focusing problem for the radially symmetric porous medium equat ion, one starts with initial data supported outside a ball centered at the origin, and studies the flow until the focusing time, i.e., until tilt: moment when the support of the solution reaches the origin. For ally fixed focusing time, say t = 0, there exists a one-parameter fam ily {g(c)(r, t)} of self similar solutions to the focusing problem. We prove that if V(r, t) is a radially symmetric porous medium pressure such that supp V (;t(o)) = [a, b] subset of R(+) for some t(o) < 0 and V focuses at t = 0, then there exist a c is an element of R(+) such that (in the appropriate technical sense) V is approximated by g(c) f or (r, t) near (0,0).