On optimal control in a model of rigid-viscoplastic media with Dirichlet boundary conditions

TL;DR

This paper investigates the optimal control problem for a 3D incompressible rigid-viscoplastic flow model of Bingham type, establishing solvability results using variational inequality methods.

Contribution

It proves the existence of solutions for the optimal control problem in a weak steady solution framework for Bingham-like media.

Findings

Existence theorem for the control problem

Application of variational inequality methods

Solution in the class of weak steady solutions

Abstract

In this paper, we consider the optimal control problem in a 3D flow model for incompressible rigid-viscoplastic media of the Bingham kind with homogeneous Dirichlet boundary conditions and a given cost functional. On the basis of methods of the theory of variational inequalities with pseudo\-monotone operators, a theorem on the solvability of the optimization problem in the class of weak steady solutions is proved.