A note on the Fujita exponent in Fractional heat equation involving the Hardy potential

In this work, we are interested on the study of the Fujita exponent and the meaning of the blow-up for the fractional Cauchy problem with the Hardy potential, namely,\begin{equation*}u_t+(-\Delta)^s u=\lambda\dfrac{u}{|x|^{2s}}+u^{p}\;{\rm in}\;{{\boldsymbol R}^N}, u(x,0)=u_{0}(x)\;{\rm in}\;{{\boldsymbol R}^N},\end{equation*}where $N> 2s$, $0 0$, $u_0\ge 0$, and $1

Keywords:

• Heat equation
• Cauchy problem
• Lambda
• Mathematical physics
• fujita exponent
• Physics

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