Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation

Shuichi Kawashima; Yu Zhu Wang

doi:10.1142/S021953051450002X

Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation

Shuichi Kawashima, Yu Zhu Wang

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

In this paper, we study the initial value problem for the generalized cubic double dispersion equation in n-dimensional space. Under a small condition on the initial data, we prove the global existence and asymptotic decay of solutions for all space dimensions n ≥ 1. Moreover, when n ≥ 2, we show that the solution can be approximated by the linear solution as time tends to infinity.

Original language	English
Pages (from-to)	233-254
Number of pages	22
Journal	Analysis and Applications
Volume	13
Issue number	3
DOIs	https://doi.org/10.1142/S021953051450002X
Publication status	Published - 2015 May 25
Externally published	Yes

Keywords

Generalized cubic double dispersion equation
asymptotic decay
global existence
linear approximation

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1142/S021953051450002X

Cite this

@article{ddd4e71ed49a4cdaace8b1017e553d2a,

title = "Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation",

abstract = "In this paper, we study the initial value problem for the generalized cubic double dispersion equation in n-dimensional space. Under a small condition on the initial data, we prove the global existence and asymptotic decay of solutions for all space dimensions n ≥ 1. Moreover, when n ≥ 2, we show that the solution can be approximated by the linear solution as time tends to infinity.",

keywords = "Generalized cubic double dispersion equation, asymptotic decay, global existence, linear approximation",

author = "Shuichi Kawashima and Wang, {Yu Zhu}",

note = "Funding Information: This work is supported in part by Grant-in-Aid for Scientific Research (A) 22244009. The second author is partially supported by the NNSF of China (Grant No. 11101144). Publisher Copyright: {\textcopyright} 2015 World Scientific Publishing Company.",

year = "2015",

month = may,

day = "25",

doi = "10.1142/S021953051450002X",

language = "English",

volume = "13",

pages = "233--254",

journal = "Analysis and Applications",

issn = "0219-5305",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "3",

}

TY - JOUR

T1 - Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation

AU - Kawashima, Shuichi

AU - Wang, Yu Zhu

N1 - Funding Information: This work is supported in part by Grant-in-Aid for Scientific Research (A) 22244009. The second author is partially supported by the NNSF of China (Grant No. 11101144). Publisher Copyright: © 2015 World Scientific Publishing Company.

PY - 2015/5/25

Y1 - 2015/5/25

N2 - In this paper, we study the initial value problem for the generalized cubic double dispersion equation in n-dimensional space. Under a small condition on the initial data, we prove the global existence and asymptotic decay of solutions for all space dimensions n ≥ 1. Moreover, when n ≥ 2, we show that the solution can be approximated by the linear solution as time tends to infinity.

AB - In this paper, we study the initial value problem for the generalized cubic double dispersion equation in n-dimensional space. Under a small condition on the initial data, we prove the global existence and asymptotic decay of solutions for all space dimensions n ≥ 1. Moreover, when n ≥ 2, we show that the solution can be approximated by the linear solution as time tends to infinity.

KW - Generalized cubic double dispersion equation

KW - asymptotic decay

KW - global existence

KW - linear approximation

UR - http://www.scopus.com/inward/record.url?scp=84928210255&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84928210255&partnerID=8YFLogxK

U2 - 10.1142/S021953051450002X

DO - 10.1142/S021953051450002X

M3 - Article

AN - SCOPUS:84928210255

SN - 0219-5305

VL - 13

SP - 233

EP - 254

JO - Analysis and Applications

JF - Analysis and Applications

IS - 3

ER -

Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this