Boundary control and observation
for an inverse coefficient problem
in the heat equation
with unknown source and initial data
报告专家：赵志学 教授（天津师范大学）
报告时间：10月17日（周六）下午17:15-18:00
报告地点：数学学院西303
报告摘要：
This talk addresses an inverse problem concerning the identification of a spatially varying diffusion coefficient in a one-dimensional heat equation with an unknown source term and initial data. The main challenges arise from the simultaneous presence of multiple unknowns and the severely limited measurement data, which consist solely of boundary control and boundary observation at a single endpoint, in addition to the inherent ill-posedness of the inverse problem. We first design an ON/OFF boundary control and prove that the diffusion coefficient can be uniquely determined from the corresponding boundary observation. We then develop a stable numerical reconstruction algorithm based on the matrix pencil method combined with an optimal perturbation regularization technique. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed identification method.
专家简介：
赵志学，天津师范大学数学科学学院教授、博士生导师，智能数学系系主任。聚焦于分布参数系统控制理论与偏微分方程反问题研究，在自动控制、应用数学等领域国内外期刊发表学术论文30余篇。先后主持国家自然科学基金项目4项，入选天津市“131”创新型人才培养工程。担任中国工业与应用数学学会智能控制与博弈专业委员会委员，以及天津市数学会理事、天津市工业与应用数学学会理事等。
邀请人：张旭
