Long-time Behavior for a Nonlinear Plate Equation with Thermal Memory

Asymptotic behavior of a thermoviscoelastic plate with memory effects

We consider a coupled linear system describing a thermoviscoelastic plate with hereditary effects. The system consists of a hyperbolic integrodifferential equation, governing the temperature, which is linearly coupled with the partial differential equation ruling the evolution of the vertical deflection, presenting a convolution term accounting for memory effects. It is also assumed that the thermal power contains a memory term characterized by a relaxation kernel. We prove that the system is exponentially stable and we obtain a closeness estimate between the system with memory effects and the…

非自治粘弹性Kirchhoff板方程的记忆效应下均匀吸引子的上半连续性

Upper-semicontinuity of uniform attractors for the non-autonomous viscoelastic Kirchhoff plate equation with memory

本文研究非自治粘弹性Kirchhoff板方程的记忆效应下均匀吸引子的上半连续性，通过能量估计和反证法证明其存在性及连续性。

受沿椭圆轨迹移动热源作用的二维板中双相滞后模型的热分析

Thermal analysis of dual-phase-lag model in a two-dimensional plate subjected to a heat source moving along elliptical trajectories

本文采用 Green 函数推导二维矩形板中沿椭圆轨迹移动点热源作用下双相滞后热传导模型的解析温度解，并分析三种轨迹下相位滞后、角速度及温度峰值的影响。

基于最终时刻测量位移识别热弹性板的热膨胀系数

Identification of thermal expansion coefficient in a thermoelastic plate from final time-measured displacement

针对耦合热弹性板系统的反问题，通过分析输入-输出算子性质，将其转化为Tikhonov泛函极小化问题，建立了极小元的存在性。

具有非线性记忆效应的四阶结构阻尼方程解的不存在性

Non-Existence of Solutions for a Fourth-Order Structurally Damped Equation Under Nonlinear Memory Effect

本文研究具有转动惯量、分数阶阻尼和记忆非线性的混合波-板方程，通过改进的检验函数论证，证明了次临界情形下任意小初始数据导致无解，以及临界情形下记忆指数大于(n-2)/n时全局解不存在。

具有分数阻尼和记忆效应的悬索桥板模型的稳定性与爆破

Stability and blow-up for a suspension bridge plate model with fractional damping and memory

研究了包含内部分数阻尼和无限记忆效应的非线性板方程描述的悬索桥模型，分析了非线性源项可能引发的不稳定性，通过半群理论建立局部解的存在性，推导了全局存在性和指数稳定性条件，证明初始能量为负时解在有限时间内爆破，展示了系统长期动力学的阈值现象。