一类四阶扩散方程解的长时间分析

Long Time Analysis of Solutions to a Fourth-order Diffusion Equation

采用构造李亚普诺夫函数的办法,对四阶扩散方程中的类退化方程进行了研究,结果表明:当时间趋于无穷大时,方程的解收敛于其初始值的均值,本质困难是最大值原理不成立.

The Liapunov functional method was used to deal with the parabolic degenerate equation in a fourth order diffusion equation. The results show that the solutions converge to their average as time tends to infinity. That the essence difficulty is the maximum value principle doesn＇t come into existence.