Speaker: 李景治教授，南方科技大学

Inviter: 刘晓东

Title: Convexification Method for Moving Targets

Language: Chinese

Time & Venue: 2026.09.15 09:00-10:00 思源楼S807

Abstract: 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.