Extinction for the super diffusion equation with a nonlocal absorption and a gradient source. (November 2016) - Zhang, Haixing; Chen, Yujuan
Abstract: In this article, the authors establish the conditions for the extinction of solutions in finite time of the super diffusion equation u t = Δ u m + λ | ∇ u | q − a ∫ Ω u p d x, m < − 1, in a bounded domain Ω ⊂ R N with N > 2 . It is shown that if 2 3 − m ≤ q < m m − 1, p < 1 + m, for sufficiently small initial data u 0, the weak solution u ( x, t ) vanishes in finite time.