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Задачи граничного управления для нелинейной модели реакции-диффузии-конвекции


Сарицкая Ж. Ю., Бризицкий Р. В.

2023, выпуск 1, С. 106-111
DOI: https://doi.org/10.47910/FEMJ202309


Аннотация
Доказана разрешимость задачи граничного управления для нелинейной модели массопереноса в случае, когда коэффициент реакции нелинейно зависит от концентрации вещества, а также зависит от пространственных переменных. Роль управления играет значение концентрации, заданное на всей границе области.

Ключевые слова: нелинейная модель массопереноса, обобщенная модель Буссинеска, коэффициент реакции, задача граничного управления.

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Библиографический список

[1] K. Ito K, K. Kunish “Estimation of the convection coefficient in elliptic equations”, Inv. Probl., 14, (1997), 995–1013.
[2] G. V. Alekseev, “Coefficient inverse extremum problems for stationary heat and mass transfer equations”, Comp. Math. Math. Phys., 47(6), (2007), 1007–1028.
[3] G. V. Alekseev, D. A. Tereshko,, “Extremum problems of boundary control for steady equations of thermal convection”, J. Appl. Mech. Tech. Phys., 51(4), (2010), 510–520.
[4] G. V. Alekseev, R. V. Brizitskii, Zh. Yu. Saritskaya, “Stability estimates of solutions to extreme problems for the nonlinear convection-diffusion-reaction equation”, Sib. J. Industr. Math., 19:2, (2016), 3–16.
[5] R. V. Brizitskii, Zh. Yu. Saritskaya, “Boundary control problem for the nonlinear convection-diffusion-reaction equation”, Comp. Math. Math. Phys., 58:12, (2018), 2139–2152.
[6] A. Yu. Chebotarev, A. E. Kovtanyuk, G. V. Grenkin, N. D. Botkin, K.-H. Hoffmann, “Non-degeneracy of optimality conditions in control problems for a radiative-conductive heat transfer model”, Appl. Math. Comp., 289, (2016), 371–380.
[7] A. Y. Chebotarev, G. V. Grenkin, A. E. Kovtanyuk, “Inhomogeneous steady-state problem of complex heat transfer”, ESAIM: Math. Model. and Num. Anal., 51:6, (2017), 2511–2519.
[8] R. V. Brizitskii, Zh. Yu. Saritskaya, “Optimization analysis of the inverse coefficient problem for the nonlinear convection-diffusion-reaction equation”, Inverse Ill-Posed Probl., 26:6, (2018), 821-833.
[9] R. V. Brizitskii, Zh. Yu. Saritskaia, “Multiplicative control problems for nonlinear reaction-diffusion-convection model”, J. Dyn. Control Systems., 27:2, (2021), 379–402.
[10] E.S. Baranovskii, “Optimal boundary control of the Boussinesq approximation for polymeric fluids”, J. Optim. Theory and Appl., 189, (2021), 623–645.
[11] G. V. Alekseev, V. G. Romanov, “One class of nonscattering acoustic shells for a model of anisotropic acoustics”, J. Appl. Industr. Math., 6 (1), (2012), 1–5.
[12] Zh.Yu. Saritskaia, “Boundary value problem for nonlinear mass-transfer equations under Dirichlet condition”, Sib. El. Math. Rep., 19:1, (2022), 360–370.
[13] S. A. Lorca, J. L. Boldrini, “Stationary solutions for generalized Boussinesq models”, J. Dif. Eq., 124, (1996), 389–406.
[14] A. Bermudez, R. Munoz-Sola, R. Vazquez, “Analysis of two stationary magnetohydrodynamics systems of equations including Joule heating”, J. Math. An. Appl., 368, (2010), 444–468.
[15] M. Ruzicka, V. Shelukhin, M. M. dos Santos, “Steady flows of Cosserat-Bingham fluids”, Math. Meth. Appl. Sc., 40, (2017), 2746–2761.
[16] A. E. Mamontov, D. A. Prokudin, “Solubility of unsteady equations of the three-dimensional motion of two-omponent viscous compressible heat-conducting fluids”, Izv. Math., 85:4, (2021), 755–812.
[17] A. E. Mamontov, D. A. Prokudin, “Global unique solvability of the initial-boundary value problem for the equations of one-dimensional polytropic flows of viscous compressible multifluids”, J. Math. Fluid Mech., 21:9, (2019), 1–9.
[18] G. V. Alekseev, “Optimization in stationary problems of heat and mass transfer and magnetic hydrodynamics.”, M.: Nauch. Mir., 2010, 412.

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