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

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• 作者：Haixing Zhang ; Yujuan Chen ; ^{cyj_nt@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Super diffusion ; Gradient source ; Absorption term ; Extinction in finite time
• 刊名：Applied Mathematics Letters
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：61
• 期：Complete
• 页码：163-166
• 全文大小：569 K

文摘

In this article, the authors establish the conditions for the extinction of solutions in finite time of the super diffusion equation u_t=Δu^m+λ|∇u|^q−a∫_Ωu^pdx,m<−1$u_t=\Delta u^m+\lambda {\left|\nabla u\right|}^q-a{\int }_{\Omega }{u}^{p}dx,m<-1$, in a bounded domain $\Omega \subset {\mathbb{R}}^N$ with N>2$N>2$. It is shown that if $\frac{2}{3-m}\le q<\frac{m}{m-1},p<1+m$, for sufficiently small initial data u₀$u_0$, the weak solution u(x,t)$u(x,t)$ vanishes in finite time.