On the behavior of solutions for a semilinear parabolic equation with supercritical nonlinearity

This paper is concerned with a Cauchy problem where and is a nonnegative radially symmetric function in with compact support. Denote the solution of (P) by . Let if and $p^{ast} = 1+6/(N-10) N geq 11 p_{ast} < p < p^{ast} lambda_{varphi} > 0 $ such that: (i) If $ lambda < lambda_{varphi} u_{lambda} $ exists globally in time in the classical sense and converges to zero locally uniformly in as . (ii) If , then $ u_{lambda} $ blows upincompletely in finite time. (iii) If , then blows upcompletely in finite time. Received: 20 December 1999; in final form: 26 May 2000 / Published online: 4 May 2001