Extinction for the super diffusion equation with a nonlocal absorption and a gradient source. (November 2016)

• Record Type: Journal Article
• Authors: Zhang, Haixing; Chen, Yujuan
• Is Part Of: Applied mathematics letters. Volume 61(2016:Nov.)
• Page Start: 163
• Page End: 166
• Publication Date: 2016-11
• Subjects: Super diffusion -- Gradient source -- Absorption term -- Extinction in finite time; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2016.06.003
• Languages: English
• ISSNs: 0893-9659

Abstract

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.