Type II blow-up for a semilinear heat equation with potential

作者：Jiang, Gui-Chun; Wang, Ruo-Yi; Wang, Yu-Xuan; Zheng, Gao-Feng^*

来源：Monatshefte für Mathematik, 2021, 195(4): 659-673.

DOI：10.1007/s00605-021-01568-y

• Quasi-monotonicity formula
• Semilinear heat equation
• Non-collapsing blow-up
• Type II blowup

Using a quasi-monotonicity formula and some energy estimates, we obtained that all non-collapsing finite time blow-up solutions to the heat equation ut=Delta u+V(x)|u|(p-1)u with 0-Dirichlet boundary value must be of type II in critical case p=pS=(N+2)/(N-2).