Analysis of the boundary value and control problems for nonlinear reaction--diffusion--convection equation

Gennady V. Alekseev ; Roman V. Brizitskii

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 4, pp. 452-462.

Résumé

The global solvability of the inhomogeneous mixed boundary value problem and control problems for the reaction–diffusion–convection equation are proved in the case when the reaction coefficient nonlinearly depends on the concentration. The maximum and minimum principles are established for the solution of the boundary value problem. The optimality systems are derived and the local stability estimates of optimal solutions are established for control problems with specific reaction coefficients.

Détail

Keywords: nonlinear reaction–diffusion–convection equation, mixed boundary conditions, maximum principle, control problems, optimality systems, local stability estimates.

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