Abstract

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

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