四阶反应扩散方程的渐近吸引子  

Asymptotic Attractor of Fourth-order Reaction-diffusion Equation

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：《中山大学学报（自然科学版）》2003年第6期15-18,共4页Acta Scientiarum Naturalium Universitatis Sunyatseni

摘　　要：研究了四阶反应扩散方程ut+αux4+ux2+u3-u=0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。This article studies the asymptotic attractor of fourth-order reaction-diffusion equation u_t+αu_(x^4)+u_(x^2)+u^3-u=0 by constructing a solution sequence.It is shown that the solution sequence doesn't go away from the global attractor in terms of mathematical induction. Then it is obtained that the solution sequence approaches to the global attractor of the equation in large time, and the dimensional estimate of the asymptotic attractor is obtained.

关 键 词：四阶反应扩散方程 渐近吸引子 有限维解序列 数学归纳法 维数估计 无穷维动力系统 

分 类 号：O19[理学—数学]