AN INVERSE PROBLEM FOR ELECTRODYNAMIC EQUATIONS WITH A NONLINEAR CONDUCTIVITY
- Authors: Romanov V.G.1
-
Affiliations:
- Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
- Issue: Vol 509, No 1 (2023)
- Pages: 65-68
- Section: МАТЕМАТИКА
- URL: https://journals.rcsi.science/2686-9543/article/view/142172
- DOI: https://doi.org/10.31857/S2686954322600719
- EDN: https://elibrary.ru/CSAJTT
- ID: 142172
Cite item
Abstract
An inverse problem of determination of a variable coefficient in electrodynamic equations with a nonlinear conductivity is considered. It is supposed that the unknown coefficient is a smooth function of space variables and finite in \({{\mathbb{R}}^{3}}\). From a homogeneous space a plane wave going in a direction fall down on a heterogeneousness. The direction is a parameter of the problem. The module of the electrical strength vector for some diapason of directions and for moments of the time close to arriving the wave at points of a surface of a ball, inside of which the heterogeneousness is contained, is given as the information for solution of the inverse problem. It is shown that this information reduces the inverse problem to the well known X-ray tomography. Algorithms of the numerical solution of the later problem is well developed.
About the authors
V. G. Romanov
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Author for correspondence.
Email: romanov@math.nsc.ru
Russian, 630090, Novosibirsk
References
- Kurylev Y., Lassas M., Uhlmann G. Invent. Math. 2018. V. 212. P. 781–857.
- Lassas M., Uhlmann G., Wang Y. Comm. Math. Phys. 2018. V. 360. P. 555–609.
- Barreto A.S. Inverse Probl. Imaging. 2020. V. 14. № 6. P. 1057–1105.
- Lassas M. Proc. Int. Congress of Math. ICM 2018, Rio de Janeiro, Brazil. 2018. V. III. P. 3739–3760.
- Stefanov P., Barreto A.S. arXiv:2102.06323. 2021.
- de Hoop M., Uhlmann G., Wang Y. Mathematische Annalen. 2020. V. 376. № 1–2. P. 765–795.
- Wang Y., Zhou T. Comm. PDE. 2019. V. 44. № 11. P. 1140–1158.
- Uhlmann G., Zhai J. Discrete Continuous Dynamical Systems - A. 2021. V. 41. № 1. P. 455–469.
- Barreto A.S., Stefanov P. arXiv: 2107.08513v1. [math. AP] 18 Jul 2021.
- Романов В.Г. Доклады АН. 2022. Т. 504. № 1. С. 36–41.
- Романов В.Г., Бугуева Т.В. Сиб. журн. индустр. матем. 2022. Т. 25. № 2. С. 83–100.
- Романов В.Г., Бугуева Т.В. Сиб. журн. индустр. матем. 2022. Т. 25. № 3. С. 154–169.
- Наттерер Ф. Математические аспекты компьютерной томографии. М.: Мир, 1990, 279 с.