New life-span results for the nonlinear heat equation

We obtain new estimates for the existence time of the maximal solutions to the nonlinear heat equation 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 upperbounds 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 & COPY; 2023 Elsevier Inc. All rights reserved.