Initial and Boundary Blow-Up Problem for \(p\) -Laplacian Parabolic Equation with General Absorption

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• 作者：Mingxin Wang ; Peter Y. H. Pang ; Yujuan Chen
• 关键词：$$p$$ p ; Laplacian parabolic equation ; Initial and boundary blow ; up ; Positive solutions ; Asymptotic behaviors ; 35K20 ; 35K60 ; 35B30 ; 35J25
• 刊名：Journal of Dynamics and Differential Equations
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：28
• 期：1
• 页码：253-279
• 全文大小：622 KB
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• 作者单位：Mingxin Wang (1)
  Peter Y. H. Pang (2)
  Yujuan Chen (3)
  
  1. Natural Science Research Center, Harbin Institute of Technology, Harbin, 150080, People’s Republic of China
  2. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore, 119076, Republic of Singapore
  3. Department of Mathematics, Nantong University, Nantong, 226007, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Ordinary Differential Equations
  Partial Differential Equations
  Applications of Mathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9222

文摘

In this article, we investigate the initial and boundary blow-up problem for the \(p\)-Laplacian parabolic equation \(u_t-\Delta _p u=-b(x,t)f(u)\) over a smooth bounded domain \(\Omega \) of \(\mathbb {R}^N\) with \(N\ge 2\), where \(\Delta _pu=\mathrm{div}(|\nabla u|^{p-2}\nabla u)\) with \(p>1\), and \(f(u)\) is a function of regular variation at infinity. We study the existence and uniqueness of positive solutions, and their asymptotic behaviors near the parabolic boundary. Keywords \(p\)-Laplacian parabolic equation Initial and boundary blow-up Positive solutions Asymptotic behaviors