Geodesic
Boundary value and extremal problems for the nonlinear convection–diffusion–reaction equation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 447-456

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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.
Mots-clés : convection-diffusion-reaction equation
Keywords: control problem, optimality system, local uniqueness. 
@article{SEMR_2015_12_a61,
     author = {R. V. Brizitskii and Zh. Yu. Saritskaya},
     title = {Boundary value and extremal problems for the nonlinear convection{\textendash}diffusion{\textendash}reaction equation},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {447--456},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a61/}
}
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R. V. Brizitskii; Zh. Yu. Saritskaya. Boundary value and extremal problems for the nonlinear convection–diffusion–reaction equation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 447-456. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a61/