nonlinear inclusion for thermo-electro-elastic: existence, dependence and optimal control

The objective of this paper is to examine a model of a thermo-electro-elastic body situated on a semi-insulator foundation. friction is characterized by tresca’s friction law, and the contact is bilateral. the primary contribution is to derive the weak variational formulation of the model, constituting a system that couples three inclusions where the unknowns are the strain field, the electric field, and the temperature field. subsequently, we demonstrate the unique solvability of the system, along with the continuous dependence of its solution under consideration. the secondary contribution involves the investigation of an associated optimal control problem, for which we establish the existence and convergence results. the proofs rely on arguments related to monotonicity, compactness, convex analysis, and lower semicontinuity.