Long Time Behavior for the Solution of the Initial-Boundary Value Problem of One Class of Systems With Multidimensional Inhomogeneous GBBM Equations

FANG Shao-mei; GUO Bo-ling

Volume 26 Issue 6

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(6): 659-664

FANG Shao-mei, GUO Bo-ling. Long Time Behavior for the Solution of the Initial-Boundary Value Problem of One Class of Systems With Multidimensional Inhomogeneous GBBM Equations[J]. Applied Mathematics and Mechanics, 2005, 26(6): 659-664.

Citation:

PDF( 2225 KB)

Long Time Behavior for the Solution of the Initial-Boundary Value Problem of One Class of Systems With Multidimensional Inhomogeneous GBBM Equations

FANG Shao-mei^1,2,
GUO Bo-ling³

1.
Department of Mathematics, Shaoguan University, Shaoguan, Guangdong 512005, P. R. China;

Received Date: 2003-11-21
Rev Recd Date: 2005-01-18
Publish Date: 2005-06-15

Abstract

Abstract

The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony (GBBM) equations is reviewed.The existence of global attractors of this problem was proved by means of a uniform a priori estimate for time.
- multidimensional GBBM equation,
- a apriori estimate,
- global attractor

FullText(HTML)

References(5)

References

[1]	GUO Bo-ling.Initial boundary value problem for one class of system of multidimensional inhomogeneous GBBM equations[J].Chinese Ann Math，Ser B,1987,8(2):226—238.
[2]	GUO Bo-ling.The global solutions of some problems for a system of equations of Schrodinger-Klein Gordon field[J].Scientia Sinica,Ser A,1982,25(3):898—901.
[3]	Temam R.Infinite Dimensional Dynamical Systems in Mechanics and Physics[M].Berlin: Springer-Verlag,1988.
[4]	Constanntin P,Foias C,Temam R.Attractors respresenting turbulent flows[J].Mem Amer Math Soc,1985,(353):364.
[5]	Babin A V, Vishik M I.Attractors of partial differential equations and estimate of their dimension[J].Uspekhi Math Nauk,1983,38：133—187.

Relative Articles

[1]	GUO Lianhong, LI Yuanfei. Continuous Dependence on Boundary Parameters of the Original Equations for LargeScale Wet Atmosphere[J]. Applied Mathematics and Mechanics, 2020, 41(9): 1036-1047. doi: 10.21656/1000-0887.410028
[2]	SU Xiaohu, JIANG Jinping. Existence of Time-Dependent Global Attractors for Beam Equations[J]. Applied Mathematics and Mechanics, 2020, 41(2): 195-203. doi: 10.21656/1000-0887.400088
[3]	YANG Mo, FU Na. Attractors of Stochastic Wave Equations With Nonlinear-Damping and Dynamic Boundary Conditions[J]. Applied Mathematics and Mechanics, 2018, 39(9): 1068-1080. doi: 10.21656/1000-0887.380254
[4]	XIAO Hai-bin. Regularity and Finite Dimensionality of Attractor for Plate Equation on Rⁿ[J]. Applied Mathematics and Mechanics, 2010, 31(11): 1372-1381. doi: 10.3879/j.issn.1000-0887.2010.11.010
[5]	FANG Shao-mei, JIN Ling-yu, GUO Bo-ling. Global Existence of Solutions of the Periodic Initial Value Problems for Two-Dimensional Newton-Boussinesq Equations[J]. Applied Mathematics and Mechanics, 2010, 31(4): 379-388. doi: 10.3879/j.issn.1000-0887.2010.04.001
[6]	FANG Shao-mei, GUO Bo-ling. Initial-Boundary Value Problem of One Class Nonlinear Schrêdinger Equations Described in Molecular Crystals[J]. Applied Mathematics and Mechanics, 2008, 29(2): 127-132.
[7]	ZHANG Rui-feng, GUO Bo-ling. Global Attractor for the Hasegawa-Mima Equation[J]. Applied Mathematics and Mechanics, 2006, 27(5): 505-511.
[8]	SHANG Ya-dong, GUO Bo-ling. Exponential Attractor for the Generalized Symmetric Regularized Long Wave Equation With Damping Term[J]. Applied Mathematics and Mechanics, 2005, 26(3): 259-266.
[9]	GU Yong-geng, SUN Wen-jun. Nontrivial Equilibrium Solutions for a Semilinear Reaction-Diffusion System[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1264-1270.
[10]	FANG Shao-mei, GUO Bo-ling. The Existence of Time Periodic Solutions for a Damped Generalized Coupled Nonlinear Wave Equations[J]. Applied Mathematics and Mechanics, 2003, 24(6): 595-604.
[11]	LIU Yu-rong, LIU Zeng-rong, ZHENG Yong-ai. Attractors of Nonautonomous Schr-dinger Equations[J]. Applied Mathematics and Mechanics, 2001, 22(2): 157-166.
[12]	TIAN Li-xin, LIU Yu-rong, LIU Zeng-rong. Local Attractors for the Weakly Damped Forced KdV Equation in Thin 2D Domains[J]. Applied Mathematics and Mechanics, 2000, 21(10): 1021-1027.
[13]	Wang Xiangdong, Han Puxian, Liang Ting. A Priori Estimate for Lower Solutions of a Class Quasilinear Elliptic Equations[J]. Applied Mathematics and Mechanics, 1999, 20(2): 217-219.
[14]	Dao Zhengde, Guo Boling, Lin Guoguang. The Fractal Structure of Attractor for the Generalized Kuramoto-Sivashinsky Equations[J]. Applied Mathematics and Mechanics, 1998, 19(3): 243-256.
[15]	Qin Wenxin, Liu Zengrong. Convergence of Attractors[J]. Applied Mathematics and Mechanics, 1997, 18(12): 1075-1080.
[16]	Wang Guanxiang, Xu Zhengyuan, Liu Zengrong. An Example of PDE with Two Attractors[J]. Applied Mathematics and Mechanics, 1995, 16(9): 775-780.
[17]	Gao Hongjun. Exponential Attractors for a Generalized Ginzburg-Landau Equation[J]. Applied Mathematics and Mechanics, 1995, 16(9): 815-820.
[18]	Tian Li-xin, Xu Zhen-yuan, Liu Zeng-rong. Attractors of Oisslpative Soliton Equation[J]. Applied Mathematics and Mechanics, 1994, 15(6): 539-547.
[19]	Liang Xi-ting, Wang Xiang-dong. A Priori Estimayes to the maximum Modulus of Generalized Solutions of a Class of Quasilinear Elliptic Epuations with Anisotropic Growth Conditions[J]. Applied Mathematics and Mechanics, 1994, 15(11): 971-980.
[20]	Liang Xi-ting, Wang Xiang-dong. A Priori Estimate for Maximum Modulus of Generalized Solutions of Quasi-Linear Elliptic Equations[J]. Applied Mathematics and Mechanics, 1990, 11(10): 881-892.