Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 66, pp. 1-13.

Title: Cauchy problem for the Lane-Emden heat flow with sign-changing initial data

Authors: Rui Huang (South China Normal Univ., Guangzhou, China)
         Shanming Ji (South China Univ. of Tech., Guangzhou, China)
         Yansheng Ma (Northeast Normal Univ., Changchun, China)

Abstract: 
This article concerns the blow-up phenomenon of sign-changing solutions
to the Lane-Emden heat flow. We construct  sign-changing weak sub-solutions 
and localization of the positive and negative parts of the sign-changing solutions.
We also extend the results to a nonlinear and finite diffusion equations.

Submitted August 22, 2024. Published October 29, 2024.
Math Subject Classifications: 35K57, 35B40, 35B44, 35K20.
Key Words: Lane-Emden heat flow; sign-changing solution; blow-up