带快速振荡项的双曲方程吸引子及其均匀化估计

Homogenization of Global Attractors for Hyperbolic Wave Equations with Rapidly Oscillating Terms

研究双曲方程utt+γεx,xεut=.(φx u)-bεx,xεf u-g x在有界光滑区域ΩRn,n≥3上的初边值问题.在一定的条件下,方程在H10×L2上具有一个紧的吸引子Aε,当ε→0时的均匀化方程也有一个吸引子A0∈H10×L2.证明了吸引子之间的一个距离distE-αAε,A0≤Cαε′,这里α′>0是一个常数.

For a smooth bounded domain Ωbekibg tiR^n ,n≥3, the authors study hyperbolic wave equation with initial problem un＋γ^ε（x,x/ε）u1=△·（φ（x）△u）-b^ε（x,x/ε）f（u）-g（x）.Under certain conditions, the equation has a compact attractor A^ε in H0^1 × L^2 , when ε→0 , homogenization equation also has a compact attractor △0∈H0^1 × L^2. This paper proves a distance of the attractors distE-α （A^ε ,A^0 ） ≤ Cε^α＇ for α＇〉 0 which is a constant.