On the asymptotic behavior of unbounded radial solutions for semilinear parabolic problems involving critical Sobolev exponent (Q994301)

The paper is dealing with a semilinear parabolic equation involving a critical Sobolev exponent in a ball or in \(\mathbb R^N\). There are two main results in this paper. The first main result is concerned with the asymptotic behavior of unbounded, radially symmetric, nonnegative global solutions in the critical case which do not decay to zero as \(t\) approaches infinity. As a by-product, the author obtains the existence of \(D_0^{1,2}\)-global bounds for unbounded global solutions. The second result involves the structure of the space of initial data in the critical case.