Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 67, pp. 1-11. Title: Existence and non-existence of solutions for Hardy parabolic equations with singular initial data Authors: Aldryn Aparcana (Univ. Nacional, San Luis Gonzaga, Ica, Peru) Brandon Carhuas-Torre (Univ. Federal de Pernambuco, Recife, Brasil) Ricardo Castillo (Univ. del Bio-Bio, Concepcion, Chile) Miguel Loayza (Univ. Federal de Pernambuco, Recife, Brasil) Abstract: We establish the existence, non-existence and uniqueness of the local solutions of the Hardy parabolic equation $u_t - \Delta u = h(t)|\cdot |^{-\gamma}g(u)$ on $\Omega \times (0,T) $ with Dirichlet boundary conditions. We assume that $\Omega$ with $0\in \Omega$ is a smooth domain bounded or unbounded, $h \in C(0,\infty)$, $g \in C([0,\infty))$ is a non-decreasing function, $0<\gamma<\min\{2,N\}$, and the initial data have a singularity at the origin. Submitted January 21, 2025. Published July 04, 2025. Math Subject Classifications: 35A01, 35A02, 35B33, 35D30, 35K58. Key Words: Local existence; Hardy parabolic equation; Lebesgue spaces; critical values; uniqueness.