Stability estimates of solutions to extremal problems for a~nonlinear convection-diffusion-reaction equation

G. V. Alekseev ; R. V. Brizitskii ; Zh. Yu. Saritskaya

Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 2, pp. 3-16.

Résumé

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 optimization. Solvability is proved of the boundary value problem and the optimization problem. In the case that the reaction coefficient is quadratic when the equation acquires cubic nonlinearity, we deduce the conditions of optimality. Analyzing the latter, we establish estimates of the local stability of solutions to the eoptimization problem under small perturbations both of the cost functional and of the given velocity vector that occurs multiplicatively in the convection-diffusion-reaction equation.

Détail

Keywords: nonlinear convection-diffusion-reaction equation, Dirichlet problem, optimal control problem, solvability, optimality conditions, stability estimate.

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