带时滞的发展方程时间依赖拉回吸引子的存在性

Existence of Time-Dependent Pullback Attractor for Evolution Equations with Delay

考虑一类带时滞的非自治二阶发展方程.首先,利用Faedo-Galerkin逼近法得到其在C_(H_(t))上解的存在性和唯一性;其次,借助算子分解验证过程{U(t,τ)}t≥τ在C_(H_(t))上的D_(C_(H_(t)))-拉回渐近紧性,从而证明带时滞的发展方程时间依赖拉回吸引子的存在性.

We considered a class of non-autonomous second-order evolution equations with delay.Firstly,we obtained the existence and uniqueness of solution by using Faedo-Galerkin approximation method in C_(H_(t)).Secondly,by means of operator decomposition,the D_(C_(H_(t)))-pullback asymptotic compactness of the process{U(t,τ)}t≥τon C_(H_(t)) was verified,which proved the existence of time-dependent pullback attractor for evolution equations with delay.