Large Time Behavior of Solutions to Semilinear Parabolic Equations with Gradient

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• 作者：Qian Zhou ; Yuanyuan Nie ; Xiaoyan Han
• 关键词：Critical Fujita exponent ; Equations with gradient
• 刊名：Journal of Dynamical and Control Systems
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：22
• 期：1
• 页码：191-205
• 全文大小：286 KB
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• 作者单位：Qian Zhou (1)
  Yuanyuan Nie (1)
  Xiaoyan Han (1)
  
  1. School of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Analysis
  Applications of Mathematics
  Systems Theory and Control
  
• 出版者：Springer Netherlands
• ISSN：1573-8698

文摘

In this paper, we investigate the large time behavior of solutions to the Cauchy problem of a class of semilinear parabolic equations with gradient. The blowing-up theorem of Fujita type is established, and the critical Fujita exponent is formulated by the spacial dimension and the behavior of the coefficient of the gradient term at ∞. It is a surprise that the critical Fujita exponent even could be 1 or infinite due to the effect of the gradient term. The critical case is also considered. An interesting phenomenon is that the critical Fujita exponent can belong to not only the blowing-up case but also the global existence case for each nontrivial solution.