Blow up of critical and subcritical norms in semilinear heat equations (Q1977684)

In the paper, the semilinear heat equation \(u_t-\Delta u=|u|^{p-1}u\) is studied in a bounded smooth domain \(\Omega\subset {\mathbb{R}}^N\) (with the Dirichlet boundary condition) or in the whole space \({\mathbb{R}}^N\), and it is supplemented with the bounded initial datum. The author proves several blow up results concerning the \(L^q\)-norm \(||u(\cdot, t)||_{L^q(\Omega)}\) for the exponent \(q\) being either subcritical or critical, i.e., \(q<N(p-1)/2\) or \(q=N(p-1)/2\).