CRITICAL FUJITA EXPONENT FOR A FAST DIFFUSIVE EQUATION WITH VARIABLE COEFFICIENTS

In this paper, we consider the positive solution to a Cauchy problem in R-N of the fast diffusive equation: vertical bar x vertical bar(m)u(t) = div(vertical bar del(u)vertical bar(p-2)del(u)) + vertical bar x vertical bar(n)(q)(u), with nontrivial, nonnegative initial data. Here 2N+m/N+m+1 < p < 2, q > 1 and 0 < m <= n < qm+N(q-1). We prove that q(c) = p-1+p+n/N+m is the critical Fujita exponent. That is, if 1 < q <= q(c), then every positive solution blows up in finite time, but for q > q(c), there exist both global and non-global solutions to the problem.