FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
The Cauchy problem in Hilbert space and its applications |
Chebotarev A.Yu. |
2025, issue 1, P. 113-121 DOI: https://doi.org/10.47910/FEMJ202510 |
Abstract |
| The nonlocal unique solvability of the abstract Cauchy problem for an equation in a Hilbert space with locally Lipschitz nonlinearity is proved. Applications of the main result to the analysis of direct and inverse problems for the Landau-Khalatnikov equation are considered. |
Keywords: Cauchy problem for a differential equation in Hilbert space, existence and uniqueness of a solution, direct and inverse problems for the Landau-Khalatnikov equation. |
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References |
| [1] Lions ZH.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, Moskva, 1972. [2] Barbu V., Nonlinear Differential Equations of Monotone Types in Banach Spaces, Springer Science-Business Media, 2010. [3] Maslovskaya A.G., Moroz L.I., Chebotarev A.Yu., Kovtanyuk A.E., “Theoretical and numerical analysis of the Landau–Khalatnikov model of ferroelectric hysteresis”, Commun Nonlinear Sci Numer Simulat, 93:105524, (2020). [4] Veselova E., Maslovskaya A., Chebotarev A., “Size-Dependent Switching in Thin Ferroelectric Films: Mathematical Aspects and Finite Element Simulation”, Computation, 11:14, (2023). |