Optimal control of a nonsmooth PDE arising in the modeling of shear–thickening fluids

This paper focuses on the analysis of an optimal control problem governed by a nonsmooth quasilinear partial differential equation that models stationary incompressible shear-thickening fluid. We start studying directional differentiability non-smooth term within state as prior step to demonstrate solution operator. Thereafter, we establish primal first order necessary optimality condition (Bouligand (B) stationarity), which is derived from By using local regularization and carrying out asymptotic thereafter, rigourously derive weak stationarity system for minima. combining B- conditions, regularity Lagrange multiplier, are able obtain strong includes characterization multiplier active inactive sets.