2025/12/20 by Michael V. Klibanov, Klibanov, Michael V., Jingzhi Li +5
Mathematics · Engineering · #Numerical methods in inverse problems #Differential Equations and Boundary Problems #Stability and Controllability of Differential Equations
paper · doi:10.48550/arxiv.2512.18361
The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and time. As the initial condition, the point source running along a straight line is used. Lateral Cauchy data are known for each position of the point source. A truncated Fourier series with respect to a special orthonormal basis is used. First, Lipschitz stability estimate is obtained. Next, a globally convergent numerical method, the so-called convexification method, is developed and its convergence analysis is carried out. The convexification method is based on a Carleman estimate. Results of numerical experiments are presented.