| Abstract: |
| We investigate a class of nonlinear elliptic boundary value problems formulated as hemivariational inequalities. These problems arise naturally in the study of steady-state heat conduction where the boundary conditions are nonmonotone and multi-valued. Such conditions are described by the Clarke generalized gradient of a locally Lipschitz continuous function on a portion of the boundary. Applying variational methods, we establish the existence of solutions for this class of inequalities [1].
In this talk, we discuss the system`s sensitivity to parameters such as the heat transfer coefficient. We present results concerning the existence of optimal solutions for related control problems and provide an asymptotic analysis showing the behavior of the system states as the parameter tends to infinity. This contribution aligns with new trends in nonlinear boundary value problems by showcasing the application of subdifferential analysis to local differential operators with complex boundary interactions.
[1] C.M. Gariboldi, S. Migorski, A. Ochal, and D.A. Tarzia, Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities, Appl. Math. Optim., 84 (Suppl 2) (2021), S1453--S1475. |
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