MATHEMATICS

On the uniqueness and stability of solutions to the control problems for the electron drift-diffusion model

R. V. Brizitskii^a, N. N. Maksimova<sup>b

a</sup> Institute of Applied Mathematics, Far East Branch of the Russian Academy of Sciences, ul. Radio, 7, Vladivostok, 690041, Russia
^b Amur State University, Ignatyevskoye shosse, 21, Blagoveshchensk, 675027, Russia

Abstract: The issues of uniqueness and stability of solutions to the control problems for the model of electron-induced charging of an inhomogeneous polar dielectric are studied. Sufficient conditions for the uniqueness and stability of optimal solutions to the considered extremum problems are established, and the local estimates of their stability with respect to small perturbations of the cost functionals are derived.

Keywords: electron drift-diffusion model, polar inhomogeneous dielectric charging model, control problem, optimality system, uniqueness of the optimal solution, local stability estimates

UDC: 517.95

MSC: 35A02, 35G30, 35R30, 49J20

Received: 29.08.2024
Accepted: 03.03.2025

DOI: 10.35634/vm250102

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