带有转动惯量和强阻尼的梁方程的时间依赖吸引子

The Time-Dependent Attractor forBeam Equation with Rotational Inertia

本文讨论了带有转动惯量梁方程: ε(t)(1 +(-Δ)α)∂t2u+Δ2u-γΔ∂tu+ f(u) = g(x),α∈[0,1)解的渐近性态,当在非线性项满足时,应用 Faedo-Galerkin 逼近方法和渐近正则估计技术,得到了解的适定性和正则性,进一步应用收缩函数方法,验证了过程的渐近紧性,最后获得了时间依赖吸引子在时间依赖空间 Htα的存在性。

In this paper, the authors study the asymptotic behavior of the solutions to the beam equation with rotational inertia and strong damping: ε(t)(1 +(-Δ)α)∂t2u+Δ2u-γΔ∂tu+ f(u) = g(x), Whereα∈[0,1). When the growth exponent of nonlinear termssatisfies firstly, by use Faedo-Galerkin approximation method and asymptotic regular estimate technique, the well-posedness and regularity of solutions are established;secondly, the asymptotic compactness of the solution process is proved via the method of contraction function;finally, the existence of time-dependent attractor is obtained in the time-dependent space Htα.