EXISTENCE AND NON-EXISTENCE OF SOLUTIONS FOR HARDY PARABOLIC EQUATIONS WITH SINGULAR INITIAL DATA

Aparcana A.; Carhuas-Torre B.; Castillo R.; Loayza M. · Electronic Journal of Differential Equations (2025) · DOI: 10.58997/ejde.2025.67

Resumen

We establish the existence, non-existence and uniqueness of the local solutions of the Hardy parabolic equation ut − ∆u = h(t)| · |−γ g(u) on Ω × (0, T) with Dirichlet boundary conditions. We assume that Ω with 0 ∈ Ω is a smooth domain bounded or unbounded, h ∈ C(0, ∞), g ∈ C([0, ∞)) is a non-decreasing function, 0 < γ < min{2, N}, and the initial data have a singularity at the origin.

Instituciones: Universidad Nacional San Luis Gonzaga