Geodesic
Stability of solutions to extremum problems for the nonlinear convection-diffusion-reaction equation with the Dirichlet condition
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2042-2053

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The solvability of the boundary value and extremum problems for the convection-diffusion-reaction equation in which the reaction coefficient depends nonlinearly on the concentration of substances is proven. The role of the control in the extremum problem is played by the boundary function in the Dirichlet condition. For a particular reaction coefficient in the extremum problem, the optimality system and estimates of the local stability of its solution to small perturbations of the quality functional and one of specified functions is established. 
@article{ZVMMF_2016_56_12_a4,
     author = {R. V. Brizitskii and Zh. Yu. Saritskaya},
     title = {Stability of solutions to extremum problems for the nonlinear convection-diffusion-reaction equation with the {Dirichlet} condition},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2042--2053},
     publisher = {mathdoc},
     volume = {56},
     number = {12},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a4/}
}
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R. V. Brizitskii; Zh. Yu. Saritskaya. Stability of solutions to extremum problems for the nonlinear convection-diffusion-reaction equation with the Dirichlet condition. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2042-2053. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a4/