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 $u_t-\hat{I}”u=|x{|}^{-{\hat{I}}^3}{u}^q$, $0<q<1$, ${\hat{I}}^3>0$ in the whole space ${\mathbb{R}}^N$, and for non-negative initial data $u_0\in C_0({\mathbb{R}}^N)$.

To appear in Tunisian Journal of Mathematics