An inhomogeneous nonlinear parabolic equation with concave nonlinearity
Abstract
We establish both the existence and uniqueness of non-negative global solutions for the nonlinear heat equation $u_t-Δu=|x|^{-γ}\,u^q$, $00$ in the whole space $\mathbb{R}^N$, and for non-negative initial data $u_0\in C_0(\mathbb{R}^N)$.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Mathematical Physics Problems
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Tunisian Journal of Mathematics
- Volume
- 8
- Issue
- 1
- Pages
- 41–58
- Publication date
- 13 January 2026
- Language
- EN