Analysis of Boundary Value and Extremum Problemsfor a Nonlinear Reaction–Diffusion–Convection Equation
Р. В. Бризицкий, V. S. Bystrova, Zh. Yu. Saritskaia
Abstract
The global solvability of boundary value problems for the reaction–diffusion–convection equation is proved for the case in which the reaction coefficient in the equation and the mass transfer coefficient in the boundary condition nonlinearly depend on the substance concentration. The minimum and maximum principle for the concentration is established. The solvability of multiplicative control problems is proved in general form. Optimality systems are derived and the presence of the bang-bang principle is established for extremum problems under the assumption that the performance functionals and the solution-dependent coefficients of the model are Fréchet differentiable.
Topics & Concepts
MathematicsMaximum principleMathematical analysisBoundary value problemMultiplicative functionPartial differential equationDifferentiable functionNonlinear systemReaction–diffusion systemOrdinary differential equationBoundary (topology)Applied mathematicsOptimal controlDifferential equationMathematical optimizationPhysicsQuantum mechanicsDifferential Equations and Numerical MethodsDifferential Equations and Boundary ProblemsNumerical methods in inverse problems