高阶广义微扰KdV方程的弱解

数学季刊 ›› 2011, Vol. 26 ›› Issue (1): 39-45.

高阶广义微扰KdV方程的弱解

School of Mathematics and Information Science, Henan Polytechnic University

收稿日期:2009-03-01 出版日期:2011-03-30 发布日期:2023-05-09
作者简介: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.
基金资助:
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)；

Weak Solution of Generalized KdV Equation with High Order Perturbation Terms

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)；

摘要/Abstract

摘要： By using the theory of compensated compactness, we prove that there exists a sequence {u^ε_δ} 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.

关键词: generalized KdV equation with high order perturbation terms, weak solution; compensated compactness

Abstract: By using the theory of compensated compactness, we prove that there exists a sequence {u^ε_δ} 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

中图分类号:

O175.25

成军祥, 王艳红. 高阶广义微扰KdV方程的弱解[J]. 数学季刊, 2011, 26(1): 39-45.

CHENG Jun-xiang, WANG Yan-hong. Weak Solution of Generalized KdV Equation with High Order Perturbation Terms [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(1): 39-45.

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