(untitled) (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 fFy+∂Φ(y) for the displacement field describes the problem in a weak formulation, where a linear mapping is represented by 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.