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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2015, Volume 12, Pages 447–456
DOI: https://doi.org/10.17377/semi.2015.12.038 (Mi semr601) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Differentical equations, dynamical systems and optimal control

Boundary value and extremal problems for the nonlinear convection–diffusion–reaction equation

R. V. Brizitskiiab, Zh. Yu. Saritskayaa

a Far Earstern Federal University, str. Sukhanova, 8, 690000, Vladivostok, Russia
b Institute of Applied Mathematics FEB RAS, str. Radio, 7, 690041, Vladivostok, Russia
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DOI: https://doi.org/10.17377/semi.2015.12.038
Abstract: We study the boundary value and optimal control problems for stationary nonlinear convection-diffusion-reaction equation, wherein reaction coefficient depends on concentration of substance. The general form of nonlinear reaction coefficient’s dependence on concentration of substance is offered. Solvability of the boundary value and control problems for convection-diffusion-reaction equation is proved. Nonlocal optimality system for the quadratic nonlinearity is obtained, and local uniqueness of extremal problem’s solution for a particular cost functional is proved with the help of optimality system.
Keywords: convection-diffusion-reaction equation, control problem, optimality system, local uniqueness.
Received June 1, 2015, published August 11, 2015
Document Type: Article
UDC: 517.95
MSC: 35A05
Language: Russian
Citation: R. V. Brizitskii, Zh. Yu. Saritskaya, “Boundary value and extremal problems for the nonlinear convection–diffusion–reaction equation”, Sib. Èlektron. Mat. Izv., 12 (2015), 447–456
Citation in format AMSBIB
\Bibitem{BriSar15}
\by R.~V.~Brizitskii, Zh.~Yu.~Saritskaya
\paper Boundary value and extremal problems for the nonlinear convection–diffusion–reaction equation
\jour Sib. \`Elektron. Mat. Izv.
\yr 2015
\vol 12
\pages 447--456
\mathnet{http://mi.mathnet.ru/semr601}
\crossref{https://doi.org/10.17377/semi.2015.12.038}
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