四阶p-广义Benney-Luke方程的初值问题

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

四阶p-广义Benney-Luke方程的初值问题

苏晓^1,*(),王书彬²()

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 Su^1,*(),Shubin Wang²()

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/Abstract

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

苏晓,王书彬. 四阶p-广义Benney-Luke方程的初值问题[J]. 数学物理学报, 2022, 42(6): 1744-1753.

Xiao Su,Shubin Wang. The Cauchy Problem for the Forth Order p-Generalized Benney-Luke Equation[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1744-1753.

参考文献 10

1	BenneyD J,LukeJ C.On the interactions of permanent waves of finite amplitude.J Math Phys,1964,43(1/4):309-313
2	PegoR L,QuinteroJ R.Two-dimensional solitary waves for a Benney-Luke equation.Physica D,1999,132(4):476-496 doi: 10.1016/S0167-2789(99)00058-5
3	QuinteroJ R.Nonlinear stability of solitary waves for a 2-D Benney-Luke equation.Discrete Cont Dyn-A,2005,13(1):203-218 doi: 10.3934/dcds.2005.13.203
4	QuinteroJ R.Existence and analyticity of lump solution for generalized Benney-Luke equations.Rev Colombiana Mat,2002,36(2):71-95
5	WangS B,XuG X,ChenG W.The Cauchy problem for the generalized Benney-Luke equation.J Math Phys,2007,48(7):073521 doi: 10.1063/1.2751280
6	GonzálezA N.The Cauchy problem for the Benney-Luke equation and generalized Benney-Luke equation.Differ Integral Equ,2007,20(12):1341-1362
7	PaumondL.A rigorous link between KP and a Benney-Luke equation.Differ Integral Equ,2003,16(9):1039-1064
8	QuinteroJ R.A remrk on the Cauchy problem for the generalized Benney-Luke equation.Differ Integral Equ,2008,21(9/10):859-890
9	BerghJ,LöfströmJ.Interpolation Spaces.New York:Springer,1976
10	LiuY.Instability and blow-up of solutions to a generalized Boussinesq equation.SIAM J Math Anal,1995,26(6):1527-1546

[1]	何鑫海,刘梅,杨晗. 一类半线性时间分数阶扩散-波动方程解的整体存在唯一性[J]. 数学物理学报, 2022, 42(6): 1705-1718.
[2]	何春蕾,刘子慧. 一类双曲平均曲率流的对称与整体解[J]. 数学物理学报, 2022, 42(4): 1089-1102.
[3]	陈翔英,陈国旺. 源于非线性层晶格模型的一耦合Boussinesq型广义方程组的Cauchy问题[J]. 数学物理学报, 2020, 40(6): 1552-1567.
[4]	肖常旺,郭飞. 一类半线性波动方程的适定性[J]. 数学物理学报, 2020, 40(6): 1568-1589.
[5]	杨柳,邓醉茶. 退化抛物型方程的一个初值反演问题[J]. 数学物理学报, 2020, 40(4): 891-903.
[6]	蒋红标,汪海航. 半线性波动方程Cauchy问题解的生命跨度估计[J]. 数学物理学报, 2019, 39(5): 1146-1157.
[7]	张淑琴, 胡雷. 含有变量阶导数及一个参数的非线性分数阶微分方程初值问题[J]. 数学物理学报, 2018, 38(2): 291-303.
[8]	叶耀军, 胡月. 一类高阶波动方程的整体解及指数衰减估计[J]. 数学物理学报, 2018, 38(1): 110-121.
[9]	苏晓, 王书彬. 任意正初始能量状态下半线性波动方程解的有限时间爆破[J]. 数学物理学报, 2017, 37(6): 1085-1093.
[10]	雷倩, 李宁, 杨晗. 梁方程解的爆破及渐近性行为[J]. 数学物理学报, 2015, 35(4): 738-747.
[11]	凌征球, 覃思乾. 非线性非局部边界条件的半线性耦合抛物型方程组[J]. 数学物理学报, 2015, 35(2): 234-244.
[12]	陈翔英. 具有弱阻尼项的广义IMBq方程初值问题解的整体存在性[J]. 数学物理学报, 2015, 35(1): 68-82.
[13]	赵伟霞. 剥脱现象中的某个自由边值问题的整体经典解[J]. 数学物理学报, 2013, 33(6): 1001-1012.
[14]	代丽美, 秦国红. Hessian商方程具有渐近性质的整体解[J]. 数学物理学报, 2012, 32(3): 566-575.
[15]	赵永祥, 肖爱国. 两步W -方法关于时滞奇异摄动初值问题的误差分析[J]. 数学物理学报, 2011, 31(5): 1239-1252.