ATTRACTOR FOR THE NON-AUTONOMOUS LONG WAVE-SHORT WAVE RESONANCE INTERACTION EQUATION WITH DAMPING

Ranran Liu; Hui Liu; Jie Xin

doi:10.11948/20190246

2020 Volume 10 Issue 3

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Ranran Liu, Hui Liu, Jie Xin. ATTRACTOR FOR THE NON-AUTONOMOUS LONG WAVE-SHORT WAVE RESONANCE INTERACTION EQUATION WITH DAMPING[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 1149-1169. doi: 10.11948/20190246

Citation:

Ranran Liu, Hui Liu, Jie Xin. ATTRACTOR FOR THE NON-AUTONOMOUS LONG WAVE-SHORT WAVE RESONANCE INTERACTION EQUATION WITH DAMPING[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 1149-1169. doi: 10.11948/20190246

ATTRACTOR FOR THE NON-AUTONOMOUS LONG WAVE-SHORT WAVE RESONANCE INTERACTION EQUATION WITH DAMPING

1.
School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China
2.
College of Information Science and Engineering, Shandong Agricultural University, Tai An, Shandong 271018, China
3.
School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, China

Corresponding author: Email address:fdxinjie@qfnu.edu.cn(J. Xin)
Fund Project: The second author was supported by the Natural Science Foundation of Shandong (Grant No. ZR2018QA002), the National Natural Science Foundation of China (No. 11901342) and China Postdoctoral Science Foundation (No. 2019M652350). The third author was supported by the NSF of China (No. 11371183) and the NSF of Shandong Province (No. ZR2013AM004)

Abstract

Abstract

In this paper, the long wave-short wave resonance interaction equation with a nonlinear term in bounded domain was studied. When $\beta\geq\frac{3}{2}$, we obtained the existence and uniqueness of the weak solution of system (1.1)-(1.4) by Galërkin's method, and further proved the existence of the compact uniform attractor for damped driven by the non-autonomous long wave-short wave resonance interaction equation.
- Long wave-short wave resonance interaction equation /
- a prioriestimates /
- well-posedness /
- attractor
MSC: 35Q55, 35B45, 34D45

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References

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