Optimization analysis of the inverse coefficient problem for the nonlinear convection-diffusion-reaction equation

Abstract

AbstractThe inverse coefficient problem for the nonlinear convection-diffusion-reaction equation is considered. A velocity vector and a mass-transfer coefficient are considered as the unknown coefficients and are recovered with the help of the additional information about the boundary value problem’s solution. The inverse coefficient problem is reduced to a two-parameter problem of multiplicative control, the solvability of which is proved in a general form. For a cubic reaction coefficient the local stability estimates of the control problem’s solutions are obtained regarding to a rather small perturbation of either the cost functional or the specified functions of the boundary value problem.