Waiting time phenomena for the porous medium equation with gradient absorption

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• 作者：Pan Zheng (1) (2)
  Chunlai Mu (1)
  Fuchen Zhang (3)
  Iftikhar Ahmed (1)
  
  1. College of Mathematics and Statistics ; Chongqing University ; Chongqing ; 401331 ; People鈥檚 Republic of China
  2. College of Mathematics and Physics ; Chongqing University of Posts and Telecommunications ; Chongqing ; 400065 ; People鈥檚 Republic of China
  3. College of Mathematics and Statistics ; Chongqing Technology and Business University ; Chongqing ; 400067 ; People鈥檚 Republic of China
  
• 关键词：Porous medium equation ; Gradient absorption ; Waiting time ; 35K55 ; 35K65 ; 35B40
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：47
• 期：1-2
• 页码：225-236
• 全文大小：167 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Theory of Computation
  Mathematics of Computing
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1865-2085

文摘

In this paper, we study the waiting time phenomena for the porous medium equation with a nonlinear gradient absorption $$\begin{aligned} u_t=\Delta u^m-|\nabla u|^q, \quad (x,t)\in \mathbb {R}^N\times (0,\infty ), \end{aligned}$$ where \(N\ge 1\) and \(m,q>1\) . According to the nonlinearity in the diffusion and the convection terms, some sufficient conditions on the initial data are given for the existence of waiting time.