Orientation Waves in a Director Field With Rotational Inertia

Attractors and their stability with respect to rotational inertia for nonlocal extensible beam equations

In this paper we consider the nonlinear beam equations accounting for rotational inertial forces. Under suitable hypotheses we prove the existence, regularity and finite dimensionality of a compact global attractor and an exponential attractor. The main purpose is to trace the behavior of solutions of the nonlinear beam equations when the effect of the rotational inertia fades away gradually. A natural question is whether there are qualitative differences would appear or not. To answer the question, we deal with the rotational inertia with a parameter alpha and consider the difference of behav…

Asymptotic profiles for damped plate equations with rotational inertia terms

We consider the Cauchy problem for plate equations with rotational inertia and frictional damping terms. We will derive asymptotic profiles of the solution in L^2-sense as time goes to infinity in the case when the initial data have high and low regularity, respectively. Especially, in the low regularity case of the initial data one encounters the regularity-loss structure of the solutions, and the analysis is more delicate. We employ the so-called Fourier splitting method combined with the explicit expression of the solutions (high frequency estimates) and the method due to Ikehata (low frequ…

关于无转动惯性的交互式流体-板系统强解的一个吸引子

On an attractor for strong solutions to interactive fluid-plate system without rotational inertia

该研究针对无转动惯性、含三维线性化Navier–Stokes方程与全von Karman板方程的非齐次流体-板耦合系统，证明了当侧向外载荷足够小时，系统强解在强相空间中存在吸引子。

带势和转动惯量项的阻尼波动方程的快速能量衰减

Fast energy decay for damped wave equations with a potential and rotational inertia terms

针对一维空间中缺乏 Hardy、Poincaré 不等式工具的困难，本文研究带势与转动惯量项的阻尼波动方程 Cauchy 问题，利用势项补偿不足，证明了解的快速能量衰减与 L^2 衰减。

A Cantilevered Extensible Beam in Axial Flow: Semigroup Well-posedness and Post-flutter Regimes

We consider a cantilevered (clamped-free) beam in an axial potential flow. Certain flow velocities may bring about a bounded-response instability in the structure, termed {\em flutter}. As a preliminary analysis, we employ the theory of {\em large deflections} and utilize a piston-theoretic approximation of the flow for appropriate parameters, yielding a nonlinear (Berger/Woinowsky-Krieger) beam equation with a non-dissipative RHS. As we obtain this structural model via a simplification, we arrive at a nonstandard nonlinear boundary condition that necessitates careful well-posedness analysis. …

具有分数阶耗散的电网与具有分数阶惯性转动的板方程耦合系统的正则性

The regularity of the coupled system between an electrical network with fractional dissipation and a plate equation with fractional inertial rotational

本文研究含分数阶转动惯性的板方程与含分数阶耗散的电网方程之强耦合系统，利用半群、频域和乘子方法刻画其解析性、Gevrey 正则性及渐近行为。