Blow-up of the critical norm for a supercritical semilinear heat equation

Hideyuki Miura, Jin Takahashi

We consider the scaling critical Lebesgue norm of blow-up solutions to the semilinear heat equation $u_t=\Delta u+|u{|}^{p-1}u$ in an arbitrary smooth domain of ${\mathbf{R}}^n$. In the rang…