Order reprints

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

*Corresponding author: Ireneo Peral ireneo.peral@uam.es

MinE2020,4,639doi:10.3934/mine.2020029

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 $N> 2s$, $0<s<1$, $(-\Delta)^s$ is the fractional laplacian of order $2s$, $\lambda >0$, $u_0\ge 0$, and $1<p<p_{+}(s,\lambda)$, where $p_{+}(\lambda, s)$ is the critical existence power to be given subsequently.