Uniform blow-up estimates for nonlinear heat equations and applications
In this survey the authors review their results on sharp uniform estimates at blow-up and on the blow-up profiles of solutions of the equation \(u_t=\Delta u + |u|^{p-1}u\) in \(\mathbb R^N\) where \(p>1\) and \((N-2)p<N+2\). Many of these results are obtained using a Liouville theorem for solutions of the above equation that are defined on \(\mathbb R^N\times (-\infty,0)\).
scientific article; zbMATH DE number 1850438