报告题目：Convexification Method for Moving Targets

报告人：李景治教授南方科技大学

报告时间：2026年07月3日10：00—11：30

报告地点：伍卓群楼三楼研讨室6

校内联系人：吕俊良 [email protected]

报告摘要：

    We formulate the problem of imaging a moving target as a nonlinear Coefficient Inverse Problem (CIP) for a hyperbolic equation with an unknown coefficient that depends on all three spatial variables and time. Using a point source running along a straight line as the initial condition, lateral Cauchy data (Dirichlet and Neumann) are measured on the boundary of a ball for each source position. A logarithmic transformation and differentiation with respect to the source parameter lead to a boundary value problem without the unknown coefficient. A truncated Fourier series with respect to a special orthonormal basis reduces the problem to a system of quasilinear hyperbolic equations. We prove a Lipschitz stability estimate and uniqueness for this system. A globally convergent numerical method—the convexification method—is developed, leveraging Carleman weight functions to ensure strong convexity of a Tikhonov-like functional. Convergence analysis is provided, and numerical experiments demonstrate the reconstruction of moving targets.

报告人简介：

    李景治，南方科技大学数学系教授。多年来一直从事逆问题相关偏微分方程数值解法的研究，在计算数学的理论研究和数值模拟方面取得了一系列的研究成果。目前主要研究领域涉及反问题理论与计算方法，形状优化与微分形式统一理论，科学计算，有限元方法。近年来，在数学物理反问题理论与计算的基础研究方面取得了一些原创性成果，包括“反问题中的若干唯一性理论”、“Carleman估计和偏微分方程反问题的凸化反演”、“反散射问题中的快速算法及其应用”等。主要研究成果发表在国内外有影响的学术刊物上（包括CMP、IP、SIAM系列、JFA、NM、MC、JDE、JCP、Sci Math China、CSIAM TAM等），主持国家省市级自然科学基金多项。