Chinese Quarterly Journal of Mathematics ›› 2011, Vol. 26 ›› Issue (1): 39-45.

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Weak Solution of Generalized KdV Equation with High Order Perturbation Terms 

  

  1. School of Mathematics and Information Science, Henan Polytechnic University
  • Received:2009-03-01 Online:2011-03-30 Published:2023-05-09
  • About author:CHENG Jun-xiang(1965- ), male, native of Wuzhi, Henan, an associate professor of Henan Polytechnic University, M.S.D., engaged in the theory of probability, the mathematical statistic teaching and research; WANG Yan-hong(1981- ), female, native of Gongyi, Henan, a lectures of Henan Polytechnic University, M.S.D., engages in partial differential equations.
  • Supported by:
    Supported by the Innovation Talents of Science and Technology of Henan University(2009-HASTIT-007); Supported by the Natural Science Program of Department of Education(2011A110006);

Abstract: By using the theory of compensated compactness, we prove that there exists a sequence {uεδ} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms, namely we prove the existence of the weak solution.

Key words: generalized KdV equation with high order perturbation terms, weak solution; compensated compactness 

CLC Number: