广义KdV-Burgers方程吸引子的谱逼近  

SPECTRAL APPROXIMATIONS OF ATTRACTORS OF GENERALIZED KdV-BURGERS EQUATIONS

作　　者：张法勇[1] 

机构地区：[1]黑龙江大学数学系,哈尔滨150080

出　　处：《高等学校计算数学学报》1999年第1期32-37,共6页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家和黑龙江自然科学基金资助项目

摘　　要：In this paper,we studied long time behavior of generalized KdV-Burgers equations by spectral method, and a semidiscrete scheme and a completely discrete scheme based on the backward Euler method are discussed. Error bounds of optimal order that hold uniformly on the unbounded time interval 0<t∞ for the semidiscrete discrete case with nonsmooth initial data, and on the finite time interval 0≤t≤ T for the completely case with nonsmooth initial data are obtained. As a corollary of the nonsmooth data error estimate, the convergence of the attractors of the corresponding approximate nonlillear semigroup generated by the semidiscrete scheme and by the completely discrete scheme is obtained.In this paper,we studied long time behavior of generalized KdV-Burgers equations by spectral method, and a semidiscrete scheme and a completely discrete scheme based on the backward Euler method are discussed. Error bounds of optimal order that hold uniformly on the unbounded time interval 0<t∞ for the semidiscrete discrete case with nonsmooth initial data, and on the finite time interval 0≤t≤ T for the completely case with nonsmooth initial data are obtained. As a corollary of the nonsmooth data error estimate, the convergence of the attractors of the corresponding approximate nonlillear semigroup generated by the semidiscrete scheme and by the completely discrete scheme is obtained.

关 键 词：KDV-B方程 广义 吸引子 谱逼近 

分 类 号：O241.82[理学—计算数学]