The parameter identification in the Stokes system with threshold slip boundary conditions

Abstract

The paper is devoted to an identification of the slip bound function g in the Stokes system with threshold slip boundary conditions assuming that g depends on the tangential velocity 𝑢𝜏 . To this end the optimal control approach is used. To remove its nonsmoothness we use a regularized form of the slip conditions in the state problem. The mutual relation between solutions to the original optimization problem and the problems with regularized states is analyzed. The paper is completed by numerical experiments.