Stability estimates of solutions to extremal problems for a nonlinear convection-diffusion-reaction equation
- Autores: Alekseev G.1,2, Brizitskii R.1,2, Saritskaya Z.2
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Afiliações:
- Institute of Applied Mathematics
- Far Eastern Federal University
- Edição: Volume 10, Nº 2 (2016)
- Páginas: 155-167
- Seção: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/212316
- DOI: https://doi.org/10.1134/S1990478916020010
- ID: 212316
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Resumo
We consider an identification problem for a stationary nonlinear convection–diffusion–reaction equation in which the reaction coefficient depends nonlinearly on the concentration of the substance. This problem is reduced to an inverse extremal problem by an optimization method. The solvability of the boundary value problem and the extremal problem is proved. In the case that the reaction coefficient is quadratic, when the equation acquires cubic nonlinearity, we deduce an optimality system. Analyzing it, we establish some estimates of the local stability of solutions to the extremal problem under small perturbations both of the quality functional and the given velocity vector which occurs multiplicatively in the convection–diffusion–reaction equation.
Sobre autores
G. Alekseev
Institute of Applied Mathematics; Far Eastern Federal University
Autor responsável pela correspondência
Email: alekseev@iam.dvo.ru
Rússia, ul. Radio 7, Vladivostok, 690041; ul. Sukhanova 8, Vladivostok, 690041
R. Brizitskii
Institute of Applied Mathematics; Far Eastern Federal University
Email: alekseev@iam.dvo.ru
Rússia, ul. Radio 7, Vladivostok, 690041; ul. Sukhanova 8, Vladivostok, 690041
Zh. Saritskaya
Far Eastern Federal University
Email: alekseev@iam.dvo.ru
Rússia, ul. Sukhanova 8, Vladivostok, 690041