Optimal Decay Rate for Degenerate
Hyperbolic-Parabolic Coupled System
报告专家：韩忠杰 教授（天津大学）
报告时间：10月17日（周六）下午15:30-16:15
报告地点：数学学院西303
报告摘要：
This talk is concerned with the explicit decay rates of a coupled PDE system composed of a wave equation and a degenerate heat equation posed on two adjoining domains. We first consider the one-dimensional setting and derive an explicit decay rate for the solutions, depending solely on the degree of degeneracy of the heat equation’s diffusion coefficient near the interface. Moreover, we show that this rate is optimal. We then investigate the system on a rectangular domain where the Geometric Control Condition (GCC) fails, and establish an explicit polynomial decay rate. Remarkably, this rate coincides with the optimal one obtained by Batty et al. [SIAM J. Math. Anal., 2018] for the corresponding systems with constant diffusion coefficients. In this sense, the decay rate derived here may also be regarded as sharp for this class of degenerate systems.
专家简介：
韩忠杰，天津大学数学学院教授、博士生导师。2010年于天津大学获博士学位，主要研究方向为分布参数系统控制理论。研究成果主要发表于SIAM J. Control and Optim., SIAM J. Appl. Math., Journal of Differential Equations, ESAIM - Control Optimisation and Calculus of Variations，IEEE Transactions on Automatic Control等控制理论及应用数学相关主流学术期刊，主持国家自然科学基金项目多项。
邀请人：张旭
