Theoretical analysis of inverse extremal problems of admixture diffusion in viscous fluids

Abstract

We consider some inverse extremal problems for the stationary equations of admixture diffusion in a viscous incompressible fluid under inhomogeneous boundary conditions for the velocity and concentration. We prove theorems on existence of solutions for the considered inverse problems, derive and analyze the optimality systems, and also establish conditions of uniqueness of their solutions for concrete objective functionals. The conditions of solvability of inverse extremal problems for the stationary Navier - Stokes equations are presented.