  We obtain new estimates for the existence time of the maximal solutions to
the nonlinear heat equation $\partial_tu-\Delta u=|u|^\alpha u,\;\alpha>0$ with
initial values in Lebesgue, weighted Lebesgue spaces or measures. Non-regular,
sign-changing, as well as non polynomial decaying initial data are considered.
The proofs of the lower-bound estimates of life-span are based on the local
construction of solutions. The proofs of the upper-bounds exploit a well-known
necessary condition for the existence of nonnegative solutions. In addition, we
establish new results for life-span using dilation methods and we give new
life-span estimates for Hardy-H\'enon parabolic equations.

Analysis of PDEs