Conley指标在偏微分方程的应用

将Conley指标应用到偏微分方程,对偏微分方程定义了孤立不变集、孤立邻域和孤立块,进而由拟指标对给出了Conley指标的定义,并对带概周期、快速振荡主部和非线性作用的非自治抛物方程,定义了孤立不变集的Conley指标。当振子的频率趋于无穷时,证明了平均自治方程的每个孤立紧不变集可以连续到非自治方程的斜积半流的孤立紧不变集上。

Conley index in Partial Differential Equations'case

This paper study Conley index in partial differential equations's case.Define isolated invariant set,isolated neighborhood and isolated block of PDE.Moreover define Conley index by quasi-index pair,and define homotopy index of isolated invariant set of non-autonomous parabolic equation with almost-period,rapidly oscillating principal part and nonlinear interaction.As the frequency of the oscillation tends to infinity,we prove that every isolated invariant set of averaged autonomous equation can continuous to an isolated invariant set of skew-product flow associated to the non-autonomous equations.