非自治强阻尼梁方程的渐近行为

Asymptotic Behavior for Non-autonomous Strongly Damped Beam Equation

研究了具有与时间相关的外力驱动的非自治强阻尼梁方程的渐近行为。当与时间有关的外力是平移紧的时候,首先利用算子半群理论证明了在一定的齐次边界条件和初值条件下系统存在连续解;再通过先验估计,构造了渐近紧的不变吸收集;最后证明了系统存在一致吸引子。

This paper presents the asymptotic behavior of solutions for the non autonomous strongly damped beam equation. When the time-dependent driving force is translation compact, the existence of the continuous solutions is proved according to the operator semigroups theory under certain homogeneous boundary conditions and initial conditions. By prior estimates, we construct the compact invariant sets. And the uniform attractor is obtained.