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

In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on a portion of the boundary described by the Clarke generalized gradient of a locally Lipschi...

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Authors: Gariboldi, Claudia M, Migórski, Stanisław, Ochal, Anna, Tarzia, Domingo A
Format: Article
Language:English
Subjects:
Asymptotic properties
Boundary conditions
Conduction heating
Conductive heat transfer
Heat flux
Heat transfer coefficients
Inequalities
Internal energy
Operators (mathematics)
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Summary:In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone 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 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.
ISSN:2331-8422