Lower bounds for the blow-up time of the heat equation in convex domains with local nonlinear boundary conditions

Xin Yang, Zhengfang Zhou

This paper studies the lower bound for the blow-up time $T^{\ast }$ of the heat equation $u_t=\Delta u$ in a bounded convex domain $\Omega$ in ${\mathbb{R}}^N(N\ge 2)$ with positive initial data…