Large time behavior of solutions for a class of time-dependent Hamilton-Jacobi equations

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• 作者：QiHuai Liu ; XinXiang Li ; Jun Yan
• 关键词：asymptotic behavior ; viscosity solution ; weak KAM theory ; Hamilton ; Jacobi equation
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：59
• 期：5
• 页码：875-890
• 全文大小：271 KB
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• 作者单位：QiHuai Liu (1) (2)
  XinXiang Li (3)
  Jun Yan (1)
  
  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China
  2. School of Mathematics and Computing Sciences, Guilin University of Electronic Technology, Guilin, 541004, China
  3. Department of Mathematics, Shanghai University, Shanghai, 200444, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

We study the long-time behavior of viscosity solutions for time-dependent Hamilton-Jacobi equations by the dynamical approach based on weak KAM (Kolmogorov-Arnold-Moser) theory due to Fathi. We establish a general convergence result for viscosity solutions and adherence of the graph as t→∞.