Research article Special Issues

Export file:

Format

• RIS(for EndNote,Reference Manager,ProCite)
• BibTex
• Text

Content

• Citation Only
• Citation and Abstract

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

1 Laboratoire d'Analyse Nonlinéaire et Mathématiques Appliquées. Département de Mathématiques, Université Abou Bakr Belkaïd, Tlemcen, Tlemcen 13000, Algeria
2 Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, Spain

This contribution is part of the Special Issue: Contemporary PDEs between theory and modeling—Dedicated to Sandro Salsa, on the occasion of his 70th birthday
Guest Editor: Gianmaria Verzini
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.