Optimal Control Approach for Bilateral Elastic Contact Problem with Power-Law Friction (Journal of Nonlinear Modeling and Analysis, 2026)
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 $f\in \mathcal{F}y+∂Φ(y)$ 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 $Φ$ is indicated by $∂Φ.$ We employ abstract existence theorems to verify the unique weak solution to the contact model.
Keywords: Optimal control approach; multivalued equation; Clarke subdifferential; elastic materials; bilateral contact problem; normal compliance condition; Coulomb dry friction (power-law friction)