四阶非线性抛物方程的渐近吸引子  

Asymptotic Attractor of Fourth Order Nonlinear Parabolic Equations

作　　者：邝雪松[1] 

机构地区：[1]湛江海洋大学基础部,广东湛江524088

出　　处：《四川大学学报（自然科学版）》2003年第3期423-429,共7页Journal of Sichuan University(Natural Science Edition)

摘　　要：考虑了四阶非线性抛物方程ut+σux4+αu+uux=f(x)的渐近吸引子,即构造了一个有限维解序列.首先利用数学归纳法证明了该解序列不会远离方程的整体吸引子;其次,证明了它在长时间后趋于方程的整体吸引子,并且给出了渐近吸引子的维数估计.The author studied the asymptotic attractor of fourth order nonlinear parabolic equations ut+σux4+αu+uux=f(x)by constructing a solution sequence.At first,it is proved that the solution sequencedoesn't go away from the global attractor in terms of mathematical induction;the second,it is proved that the solution sequence approaches to the global attractor of the equation in large time,and the dimemsional estimate of the asymptoticattractor is obtained.

关 键 词：四阶非线性抛物方程 解序列 渐近吸引子 

分 类 号：O175[理学—数学]