Convexification numerical method for imaging of moving targets

Convexification numerical method for imaging of moving targets Full article

Journal

Mathematische Annalen
ISSN: 0025-5831 , E-ISSN: 1432-1807

Output data

Year: 2026, Volume: 396, Number: 1, Article number : 25, Pages count : 38 DOI: 10.1007/s00208-026-03565-8

Authors

Klibanov Michael V. ¹ , Li Jingzhi ² , Romanov Vladimir G. ³ , Yang Zhipeng ⁴

Affiliations

1	Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC, 28223, USA
2	Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, People’s Republic of China
3	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
4	School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

Funding (1)

Министерство науки и высшего образования РФ

FWNF-2026-0029

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, aglobally convergent numericalmethod, 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.

Klibanov M.V. , Li J. , Romanov V.G. , Yang Z.
Convexification numerical method for imaging of moving targets
Mathematische Annalen. 2026. V.396. N1. 25 :1-38. DOI: 10.1007/s00208-026-03565-8 WOS OpenAlex

Submitted:	Dec 21, 2025
Accepted:	Aug 14, 2026
Published online:	Aug 30, 2026

≡ Web of science:	WOS:001862454700001
≡ OpenAlex:	W7117151366