Global existence and blowup for sign-changing solutions of the nonlinear heat equation (Q1014717)

Given \(0<\alpha<2/N\), it is proved that a function \(\psi\) exists with the following properties: The solution of the equation \(u_t+\Delta u=|u|^\alpha u\) in \(\mathbb{R}^N\) with the initial condition \(\psi\) is global while the solution with the initial condition \(\lambda\psi\) blows up in finite time if \(\lambda >0\) is either sufficiently small or sufficiently large.