Let $p>1$ be an even number and $\Omega\subset R^3$ be a bounded boundary $\partial\Omega$. Using an energy argument to show that the classical solution $u$ to IBVP \begin{equation} \left\{\begin{array}{lll} u_t=\Delta u+u^p, & x \in \Omega, & t>0, \\ \frac{\partial u}{\partial \nu}=0, & x \in \partial \Omega, & t>0, \\ u(x, 0)=u_0(x), & x \in \Omega, & \end{array}\right. \end{equation} must blow up in a finite time provided that $u_0(x)$ is nonnegative and $\int_\Omega u_0(x)dx>0$.
I am stuck in it, how to deal with it? Are there some conferences?