一类四阶抛物型方程的解的渐近行为

The Asymptotic Behavior of the Solution of a Fourth order Parabolic Equation

本文考虑一维空间中四阶抛物型方程Cauchy问题■的整体解u=(x,t)的大时间渐近行为和时间衰减速率。

In this paper, we consider the large time behavior and the time-decay rate of global solutions to the Cauchy problem of fourth order parabolic equation in one dimension space：{u（x,0）=u0（x）,ut=эx^2u＋эx^4u=эxf（u）,x∈R,x∈R,t〉0,with f（u）satisfying f（u）∈C^1（R）,｜f（u）｜≤C｜u｜^q,q〉2^-5.