Multiplicative control problems for nonlinear convection-diffusion-reaction equation. (English) Zbl 1433.49004
Summary: The problem for convection-diffusion-reaction equation, in which reaction coefficient depends nonlinearly on substance’s concentration, is considered. Velocity vector, multiplicatively entered into the considered equation, is chosen as a control function. Extremum problem’s solvability for reaction coefficient of common type is proved. Optimality system for quadratic reaction coefficient is obtained and on its basis local uniqueness of control problem’s solutions for particular cost functionals is proved.
MSC:
49J20 | Existence theories for optimal control problems involving partial differential equations |
35J57 | Boundary value problems for second-order elliptic systems |