Phuc Cong Nguyen

Optimal global well-posedness for semilinear heat equations

We address the question of global in time existence for the semilinear parabolic equation \begin{equation*} \left\{ \begin{array}{rcl} \partial_t u-\Delta u&=&|u|^{b-1}u \quad {\rm ~in~} \mathbb{R}^n\times (0,\infty),\\ u(\cdot,0)&=&u_0 \quad {\rm ~in~} \mathbb{R}^n, \end{array} \right. \end{equation*} where $b>1+2/n,...