THE INERTIAL FRACTAL SET FOR WEAKLY DAMPED FORCEDKORTEWEG-DE-VRIES EQUATION

Applied Mathematics and Mechanics (English Edition) ›› 1995, Vol. 16 ›› Issue (1): 37-45.

THE INERTIAL FRACTAL SET FOR WEAKLY DAMPED FORCEDKORTEWEG-DE-VRIES EQUATION

戴正德¹, 朱智伟²

1. Instilute of Applied Mathematics, Yunnan Province, Department of Math., Yunnan Univ, Kunming;
2. Department of Math., Xijang University

收稿日期:1994-04-30 出版日期:1995-01-18 发布日期:1995-01-18
基金资助:
Project supported by National Natural Science Foundation of China

THE INERTIAL FRACTAL SET FOR WEAKLY DAMPED FORCEDKORTEWEG-DE-VRIES EQUATION

Dai Zheng-de¹, Zhu Zhi-wei²

1. Instilute of Applied Mathematics, Yunnan Province, Department of Math., Yunnan Univ, Kunming;
2. Department of Math., Xijang University

Received:1994-04-30 Online:1995-01-18 Published:1995-01-18
Supported by:
Project supported by National Natural Science Foundation of China

摘要/Abstract

摘要： In this paper we consider weakly damped forced Korteweg-de-Vries equation withnon-self-adjoint operator. The existence of inertial fractal set M of this equation is proved, the estimates of the upper bounds of fractal dimension for M are alsoobtained.

关键词: truncated shallow conical sandwich shells with variable thickness, nonlinear stability, modified iteration method, KdV equation, inertial fractal, dimension

Abstract: In this paper we consider weakly damped forced Korteweg-de-Vries equation withnon-self-adjoint operator. The existence of inertial fractal set M of this equation is proved, the estimates of the upper bounds of fractal dimension for M are alsoobtained.

Key words: truncated shallow conical sandwich shells with variable thickness, nonlinear stability, modified iteration method, KdV equation, inertial fractal, dimension

戴正德;朱智伟. THE INERTIAL FRACTAL SET FOR WEAKLY DAMPED FORCEDKORTEWEG-DE-VRIES EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 1995, 16(1): 37-45.

Dai Zheng-de;Zhu Zhi-wei. THE INERTIAL FRACTAL SET FOR WEAKLY DAMPED FORCEDKORTEWEG-DE-VRIES EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 1995, 16(1): 37-45.

[1]	Shuangpeng LI, Ruoran CHENG, Nannan MA, Chunli ZHANG. Analysis of piezoelectric semiconductor fibers under gradient temperature changes[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(2): 311-320.
[2]	Jing ZHANG, Guanting LIU. A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(9): 1533-1546.
[3]	Zhiping MAO, Xuhui MENG. Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(7): 1069-1084.
[4]	Huayang DANG, Dongpei QI, Minghao ZHAO, Cuiying FAN, C.S. LU. Thermal-induced interfacial behavior of a thin one-dimensional hexagonal quasicrystal film[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 841-856.
[5]	Wei CHEN, Guozhen WANG, Yiqun LI, Lin WANG, Zhouping YIN. The quaternion beam model for hard-magnetic flexible cantilevers[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 787-808.
[6]	M. HAMID, M. USMAN, Zhenfu TIAN. Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD flows[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(4): 669-692.
[7]	A. V. ROŞCA, N. C. ROŞCA, I. POP. Three-dimensional mixed convection stagnation-point flow past a vertical surface with second-order slip velocity[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(4): 641-652.
[8]	Zhimin CHEN, W. G. PRICE. Secondary steady-state and time-periodic flows from a basic flow with square array of odd number of vortices[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(3): 447-458.
[9]	Xiaoyu FU, Xiang MU, Jinming ZHANG, Liangliang ZHANG, Yang GAO. Green’s functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(2): 237-254.
[10]	Xinte WANG, Juan LIU, Biao HU, Bo ZHANG, Huoming SHEN. Wave propagation responses of porous bi-directional functionally graded magneto-electro-elastic nanoshells via nonlocal strain gradient theory[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(10): 1821-1840.
[11]	Huimin CHEN, Qingzhuo CHI, Ying HE, Lizhong MU, Yong LUAN. Effects of size and location of distal tear on hemodynamics and wave propagation in type B aortic dissection[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(9): 1449-1468.
[12]	Zhenni LI, Yize WANG, Yuesheng WANG. Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(2): 167-184.
[13]	Xin ZHANG, Minghao ZHAO, Cuiying FAN, C. S. LU, Huayang DANG. Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(12): 1901-1920.
[14]	P. SINGH, A. K. SINGH, A. CHATTOPADHYAY. Reflection of three-dimensional plane waves at the free surface of a rotating triclinic half-space under the context of generalized thermoelasticity[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(9): 1363-1378.
[15]	Tuoya SUN, Junhong GUO, E. PAN. Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(8): 1077-1094.

THE INERTIAL FRACTAL SET FOR WEAKLY DAMPED FORCEDKORTEWEG-DE-VRIES EQUATION

THE INERTIAL FRACTAL SET FOR WEAKLY DAMPED FORCEDKORTEWEG-DE-VRIES EQUATION

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价