LIFE SPAN OF SOLUTIONS FOR A FAST DIFFUSION EQUATION WITH SOURCE
This paper is concerned with the Cauchy problem for the fast diffusion equation in where and The initial condition is assumed to be continuous, nonnegative and bounded. For the non-decaying initial data, it is well known that the solution blows up in finite time. We give a new upper bound of the life span of positive solutions for the non-decaying initial data. It is also shown that the solution blows up at minimal blow-up time when the initial data attain its maximum at space infinity.
life span, quasilinear parabolic equation, Cauchy problem, non-decaying initial data, blow-up.