EXISTENCE AND ASYMPTOTIC BEHAVIOR OF TRAVELING WAVE SOLUTION FOR KORTEWEG-DE VRIES-BURGERS EQUATION WITH DISTRIBUTED DELAY

Jingdong Wei; Jiangbo Zhou; Lixin Tian

doi:10.11948/2156-907X.20180017

2019 Volume 9 Issue 3

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Jingdong Wei, Jiangbo Zhou, Lixin Tian. EXISTENCE AND ASYMPTOTIC BEHAVIOR OF TRAVELING WAVE SOLUTION FOR KORTEWEG-DE VRIES-BURGERS EQUATION WITH DISTRIBUTED DELAY[J]. Journal of Applied Analysis & Computation, 2019, 9(3): 840-852. doi: 10.11948/2156-907X.20180017

Citation:

Jingdong Wei, Jiangbo Zhou, Lixin Tian. EXISTENCE AND ASYMPTOTIC BEHAVIOR OF TRAVELING WAVE SOLUTION FOR KORTEWEG-DE VRIES-BURGERS EQUATION WITH DISTRIBUTED DELAY[J]. Journal of Applied Analysis & Computation, 2019, 9(3): 840-852. doi: 10.11948/2156-907X.20180017

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF TRAVELING WAVE SOLUTION FOR KORTEWEG-DE VRIES-BURGERS EQUATION WITH DISTRIBUTED DELAY

1.
Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, China
2.
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, Jiangsu, China

Corresponding author: Email address:ujszjb@126.com(J. Zhou)
Fund Project: The authors are deeply grateful to the anonymous referees for the valuable suggestions and comments which have greatly improved the presentation of our paper. The authors were supported by the China Postdoctoral Science Foundation (No. 2018M642174) and the National Natural Science Foundation of China (Nos. 71690242, 91546118 & 11731014)

Abstract

Abstract

In this paper, we investigate the existence and asymptotic behavior of traveling wave solution for delayed Korteweg-de Vries-Burgers (KdV-Burgers) equation. Using geometric singular perturbation theory and Fredholm alternative, we establish the existence of traveling wave solution for this equation. Employing the standard asymptotic theory, we obtain asymptotic behavior of traveling wave solution of the equation.
- Delayed Korteweg-de Vries-Burgers equation /
- traveling wave solution /
- geometric singular perturbation theory /
- asymptotic behavior
MSC: 34E15, 34D15, 35Q53, 35C07

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References

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