The aim goal of this paper is to treat the following problem \begin{ equation*} \left\{ \begin{ array}{ rcll} u_t+(-\D^s_{ p}) u &=&\dyle \l \dfrac{ u^{ p-1}}{ |x|^{ ps}} & \text{ in } \O_{ T}=\Omega \times (0,T), \\ u&\ge & 0 & \text{ in }\ren \times (0,T), \\ u &=& 0 & \text{ in }(\ren\setminus\O) \times (0,T), \\ u(x,0)&=& u_0(x)& \mbox{ in }\O, \end{ array}% \right. \end{ equation*} where $\Omega$ is a bounded domain containing the origin, $$ (-\D^s_{ p})\, u(x,t):=P.V\int_{ \ren} \,\dfrac{ |u(x,t)-u(y,t)|^{ p-2}(u(x,t)-u(y,t))}{ |x-y|^{ N+ps}} \,dy$$ with $1<p<N, s\in (0,1)$ and $f, u_0$ are non negative functions. The main goal of this work is to discuss the existence of solution according to the values of $p$ and $\l$.
Categories: math.AP