On the existence and nonexistence of global solutions of the semilinear heat equation

Kaiqiang Zhang, Zhiyu Li

We consider the semilinear heat equation $$u_t-\hat{I}”u=|u{|}^{p-1}u,(t,x)\in {\mathbb{R}}^{+}\times {\mathbb{R}}^n.$$ The well-known difficulty with this problem is that the potential well…