数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1744-1753.

• 论文 • 上一篇    下一篇

四阶p-广义Benney-Luke方程的初值问题

苏晓1,*(),王书彬2()   

  1. 1 河南工业大学理学院, 郑州 450001
    2 郑州大学数学与统计学院, 郑州 450001
  • 收稿日期:2021-10-26 出版日期:2022-12-26 发布日期:2022-12-16
  • 通讯作者: 苏晓 E-mail:sx19873@163.com;wangshubin@zzu.edu.cn
  • 作者简介:王书彬, E-mail: wangshubin@zzu.edu.cn
  • 基金资助:
    河南省自然科学基金资助项目(202300410109);河南工业大学河南省省属高校基本科研业务费专项资金(2018QNJH19);河南工业大学青年骨干教师培育计划

The Cauchy Problem for the Forth Order p-Generalized Benney-Luke Equation

Xiao Su1,*(),Shubin Wang2()   

  1. 1 College of Science, Henan University of Technology, Zhengzhou 450001
    2 School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001
  • Received:2021-10-26 Online:2022-12-26 Published:2022-12-16
  • Contact: Xiao Su E-mail:sx19873@163.com;wangshubin@zzu.edu.cn
  • Supported by:
    the Natural Science Foundation of Henan(202300410109);the Fundamental Research Funds for the Henan Provincial Colleges and Universities in Henan University of Technology(2018QNJH19);the training plan for young backbone teachers of Henan University of Technology

摘要:

研究了四阶p-广义Benney-Luke方程的初值问题在自然能量空间$\dot{H}^{1}(\mathbb{R}^n)\cap\dot{H}^{2}(\mathbb{R}^n)\times H^1(\mathbb{R}^n)$中解的整体存在性和唯一性.首先利用压缩映像原理证明解在能量空间中的局部存在性和唯一性.其次当非线性项为源项时给出解整体存在的充分条件.

关键词: $p$-广义Benney-Luke方程, 初值问题, 整体解

Abstract:

We consider the global existence and uniqueness of the Cauchy problem for the forth order $p$-generalized Benney Luke equatoion in the natural energy space $\dot{H}^{1}(\mathbb{R}^n)\cap\dot{H}^{2}(\mathbb{R}^n) \times H^1(\mathbb{R}^n)$. First of all, the local existence and uniqueness of solutions are investigated in the energy space by means of the contraction mapping principle. Secondly, in the case of source nonlinearity, we provide the sufficient conditions of the existence of global solutions.

Key words: $p$-generalized Benney-Luke equation, Cauchy problem, Global solutions

中图分类号: 

  • O175.29