Session S01 - Modeling and Computation for Control and Optimization of Biological and Physical Systems

Wednesday, July 14, 16:00 ~ 16:25 UTC-3

Existence, comparison, monotonicity and convergence results for a class of elliptic hemivariational inequalities

Domingo Alberto Tarzia

Universidad Austral and CONICET, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with non-monotone multivalued subdifferential boundary condition on a portion of the boundary described by the Clarke generalized gradient of a locally Lipschitz function. First, we prove a new existence result for the inequality employing the theory of pseudomonotone operators. Next, we give a result on comparison and monotonicity of solutions, and provide sufficient conditions that guarantee the asymptotic behavior of solution, when the heat transfer coefficient tends to infinity. Further, we show a result on the continuous dependence of solution on the internal energy and heat flux. Finally, some examples of convex and nonconvex potentials illustrate our hypotheses.

Joint work with Claudia M. Gariboldi (Universidad Nacional de Río Cuarto, Argentina), Stanislaw Migórski (Jagiellonian University, Poland) and Anna Ochal (Jagiellonian University, Poland).

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