THE CAUCHY-PROBLEM FOR VARIABLE-COEFFICIENT POROUS-MEDIUM EQUATIONS

We study the class of non-negative continuous weak solutions of the Ge neralized Porous Medium equations partial derivative u/partial derivat ive t = Delta phi(x,t,u), (x,t) epsilon R-n x (0,T), where n greater t han or equal to 1 and 0 < T less than or equal to infinity. We give a complete description of solutions in terms of existence, uniqueness, e xistence of initial trace and blow up.