四阶p-广义Benney-Luke方程的初值问题

Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1744-1753.

Previous Articles Next Articles

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

Abstract

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

CLC Number:

O175.29

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.

Trendmd

References 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]	Xinhai He,Mei Liu,Han Yang. Existence and Uniqueness of Global Solutions for a Class of Semilinear Time Fractional Diffusion-Wave Equations [J]. Acta mathematica scientia,Series A, 2022, 42(6): 1705-1718.
[2]	Hongwu Zhang. One Regularization Method for a Cauchy Problem of Semilinear Elliptic Equation [J]. Acta mathematica scientia,Series A, 2022, 42(1): 45-57.
[3]	Xiangying Chen,Guowang Chen. Cauchy Problem for a Generalized System of Coupled Boussinesq Type Equations Arising from Nonlinear Layered Lattice Model [J]. Acta mathematica scientia,Series A, 2020, 40(6): 1552-1567.
[4]	Wang Li. The Inverse Problem for the Supersonic Plane Flow Past a Curved Wedge [J]. Acta mathematica scientia,Series A, 2018, 38(4): 679-686.
[5]	Xie Ou, Meng Zehong, Zhao Zhenyu, You Lei. A Truncation Method Based on Hermite Functions Expansion for a Cauchy Problem of the Laplace Equation [J]. Acta mathematica scientia,Series A, 2017, 37(3): 457-468.
[6]	Deng Jiqin, Deng Ziming. Existence and Uniqueness of Solutions for Nonlocal Cauchy Problem for Fractional Evolution Equations [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1157-1164.
[7]	Lei Qian, Li Ning, Yang Han. Blow Up and Asymptotic Behavior in the Beam Equation [J]. Acta mathematica scientia,Series A, 2015, 35(4): 738-747.
[8]	CHEN Xiang-Ying. Global Existence of Solution of Cauchy Problem for A Generalized IMBq Equation with Weak Damping [J]. Acta mathematica scientia,Series A, 2015, 35(1): 68-82.
[9]	ZHU Xu-Sheng, LI Fang-E. The Global Solutions of the Compressible Euler Equations With Nonlinear Damping in 3-Dimensions [J]. Acta mathematica scientia,Series A, 2014, 34(5): 1111-1122.
[10]	SHEN Ji-Hong, ZHANG Ming-You, YANG Yan-Bing, LIU Bo-Wei, XU Run-Zhang. Global Well-posedness of Cauchy Problem for Damped Multidimensional Generalized Boussinesq Equations [J]. Acta mathematica scientia,Series A, 2014, 34(5): 1173-1187.
[11]	SHU Xiao-Bao, DAI Bin-Xiang. S-asymptotically ω-periodic Solutions of Semi-linear Neutral Fractional Differential Equations [J]. Acta mathematica scientia,Series A, 2014, 34(1): 16-26.
[12]	XU Hong-Mei, XU Ying-Ying. Pointwise Estimates of Solutions of Generalized Benjamin-Bona-Mahony Equations in Multi Dimensions [J]. Acta mathematica scientia,Series A, 2013, 33(6): 1112-1121.
[13]	ZHANG Quan-Ju. The Cauchy Problems of a class of Equations \|for the Tension of Extensible Beam [J]. Acta mathematica scientia,Series A, 2003, 23(6): 704-710.
[14]	Qin Yuming. Global Exisence of Classical Solution to the Nonlinear Wave Equations [J]. Acta mathematica scientia,Series A, 1997, 17(2): 121-128.

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

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References 10

Related Articles 14

Metrics

Comments

Recommended 10