Optimal Control Approach for Bilateral Elastic Contact Problem with Power-Law Friction

Abstract

We use the control variational technique to examine an elastic contact model, subject to a non-penetration condition in the normal direction and to power-law friction, proving the unique existence of the solution. This method uses optimal control theory to minimize the energy functional of the nonlinear equation. A multivalued equation $f\in \mathcal{F}y+∂\Phi(y)$ for the displacement field describes the problem in a weak formulation, where a linear mapping is represented by $\mathcal{F},$ and the Clarke’s subdifferential of the mapping $\Phi$ is indicated by $∂\Phi.$ We employ abstract existence theorems to verify the unique weak solution to the contact model.