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Russia Blagoveshchensk; Vladivostok
Year
2024
Volume
34
Issue
1
Pages
3-18
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Section Mathematics
Title On the uniqueness of a solution to the multiplicative control problem for the electron drift–diffusion model
Author(-s) Brizitskii R.V.ab, Maksimova N.N.c
Affiliations Far Eastern Federal Universitya, Institute of Applied Mathematics, Far East Branch of the Russian Academy of Sciencesb, Amur State Universityc
Abstract The multiplicative control problem for a stationary diffusion-drift model of charging a polar dielectric is studied. The role of control is played by a leading coefficient in the model equation, which has the meaning of the electron diffusion coefficient. The global solvability of the boundary value problem and the local uniqueness of its solution, as well as the solvability of the extremum problem under consideration, have been proved in the previous papers of the authors. In this paper, an optimality system is derived for the control problem and local regularity conditions for the Lagrange multiplier are established. Based on the analysis of this system, the local uniqueness of the multiplicative control problem's solution for specific cost functionals is proved.
Keywords electron drift–diffusion model, polar dielectric charging model, multiplicative control problem, optimality system, local uniqueness
UDC 517.95
MSC 35A02, 35G30, 35R30, 49J20
DOI 10.35634/vm240101
Received 6 July 2023
Language Russian
Citation Brizitskii R.V., Maksimova N.N. On the uniqueness of a solution to the multiplicative control problem for the electron drift–diffusion model, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2024, vol. 34, issue 1, pp. 3-18.
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