An inhomogeneous nonlinear parabolic equation with concave nonlinearity

We establish both the existence and uniqueness of non-negative global solutions for the nonlinear heat equation $u_t-Δu=|x|^{-γ}\,u^q$, $0<q<1$, $γ>0$ in the whole space $\mathbb{R}^N$, and for non-negative initial data $u_0\in C_0(\mathbb{R}^N)$.

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