Liouville theorem for subcritical nonlinear heat equation

We obtain a Li-Yau-type estimate for nonnegative ancient solutions to the subcritical semilinear heat equation $\frac{\text{p}u}{\text{p}t}=\text{De}u+u^p$ in ${\text{rz}}^n\times (-\mathrm{\infty },0)$. Then, we combine the Li-Yau type estimate and Melre-Zaag’s result to prove the Liouville theorem of this equation.