Acta Mathematica Scientia

, Volume 39, Issue 1, pp 180–194 | Cite as

Global Existence and Pointwise Estimates of Solutions to Generalized Kuramoto-Sivashinsky System in Multi-Dimensions

  • Yingshu Zhang (张颖姝)
  • Lang Li (李朗)
  • Shaomei Fang (房少梅)Email author


The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multi-dimensions (n ≥ 3) is considered. Based on Green’s function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the Lp convergence rate of the solution is obtained.

Key words

Kuramoto-Sivashinsky equation global existence pointwise estimates Green’s function method energy method 

2010 MR Subject Classification

35A01 35E15 


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Copyright information

© Wuhan Institutes of Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  • Yingshu Zhang (张颖姝)
    • 1
  • Lang Li (李朗)
    • 1
  • Shaomei Fang (房少梅)
    • 1
    Email author
  1. 1.Department of MathematicsSouth China Agricultural UniversityGuangzhouChina

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