山西大学数学与统计学院学术报告

This talk studies a transmission model of coupled wave equation and Kirchhoff-type

wave equation in different domains through a common boundary, in which

viscoelastic material is pasted into the edge of the Kirchhoff-type wave

equation. When the kernel function satisfies a second-order nonlinear

ordinary differential equation, applying inverse Volterra’s operator and

the Riemannian geometry method, we establish the general decay result

which is given by solutions of a first order nonlinear, dissipative ODE

under some conditions on the coefficient matrix, and which is not necessarily

decaying in a polynomial or exponential fashion. In this talk, we will

discuss the boundary controllability of a class of coupled system consisting

of several inhomogeneous plates with clamped boundary conditions and the

hinge boundary conditions. By using the Riemannian geometry approach,

the duality method, the multiplier technique and a compact perturbation

method, we finally prove that the plate system is exactly null controllable

under some verifiable geometrical assumptions.

邓丽，女，西南交通大学数学学院教授，博士生导师。近年的研究主要集中于黎曼流形上控制系统的最优控制与稳定性理论。

相关研究成果已发表在 ESAIM: COCV、SIAM J. Control Optim.、J. Differential Equations、Sci. China Math. 等期刊。近期，报告人进一步研究了黎曼流形上常微分方程的 Lyapunov 稳定性与输入状态稳定性问题，给出了依赖于黎曼度量的平衡点吸引域估计。

刘玉香，女，青岛理工大学理学院副教授，硕士生导师。主持完成国家自然科学基金青年项目和山东省自然科学基金博士项目各一项，在SIAM J. Control Optim.、Appl. Math. Optim.、J. Math. Anal. Appl.、Nonlinear Anal. Real World Appl.等期刊发表论文10余篇。

杨峰艳，女，北京林业大学理学院副教授。已主持完成中央高校专项项目1项，现主持国家自然科学基金青年项目1项。

在Mathematics of Control, Signals and Systems、Evolution Equations and Control Theory、Electronic Journal of Differential Equations、Applied Mathematics Optimization、Journal of Mathematical Analysis and Applications、Advances in Nonlinear Analysis等期刊上发表论文10余篇.