Extinction for the super diffusion equation with a nonlocal absorption and a gradient source

In this article, the authors establish the conditions for the extinction of solutions in finite time of the super diffusion equation ut=Δum+λ|∇u|q−a∫Ωupdx,m<−1ut=Δum+λ|∇u|q−a∫Ωupdx,m<−1, in a bounded domain Ω⊂RN with N>2N>2. It is shown that if 23−m≤q