Life Span of Solutions for a Semilinear Heat Equation with Initial Data Non-Rarefied at $\mathrm{\infty }$

We study the Cauchy problem for a semilinear heat equation with initial data non-rarefied at $\mathrm{\infty }$. Our interest lies in the discussion of the effect of the non-rarefied factors on the life span of solutions, and some sharp estimates on the life span is established.