Local existence and nonexistence of solutions to the Hardy parabolic equation with general nonlinearity
Abstract
In this paper, we consider the Cauchy problem for the Hardy parabolic equation with general nonlinearity and establish the local existence and nonexistence results. Our results provide the optimal integrability conditions on initial function for the existence of a local-in-time nonnegative solution. The proof of the existence result is based on the supersolution method.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Differential Equations and Boundary Problems
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 30 January 2026
- Document type
- Preprint