Global solution and blowup of semilinear heat equation with critical Sobolev exponent

In this paper, we have two folds: first, we are concerned with the existence and asymptotic estimates of global solutions and blowup of semilinear heat equation of the following form: {u(t) - Deltau = u(p), (x, t) is an element of Omega x (0, T), {u(x, t) = 0, (x, t) is an element of partial derivative Omega x (0, T), {u(x, 0) = u(0)(x), u(0)(x) greater than or equal to 0, u(0)(x) not equivalent to 0, with lower-energy initial value, and using Moser-type iteration it is then proved that the global H-0(1)(Omega) solutions with lower-energy initial value are classical global solutions for all t greater than or equal to t(0) > (.) Here Omega is a bounded domain in R-N (N greater than or equal to 3), and p = 2* - 1 = (N+2)/(N-2) 2* is the critical Sobolev exponent. The second is to consider the asymptotic behavior of any global solutions that may possess high-energy initial value, and apply the idea to describe exactly the asymptotic profile of the unbounded, global solution, which was first obtained by Ni et al.