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:Applied mathematics & optimization 2021-12, Vol.84 (Suppl 2), p.1453-1475
Main Authors: Gariboldi, Claudia M., Migórski, Stanisław, Ochal, Anna, Tarzia, Domingo A.
Format: Article
Language:English
Subjects:
Applied mathematics
Asymptotic properties
Boundary conditions
Calculus of Variations and Optimal Control
Optimization
Conduction heating
Conductive heat transfer
Control
Heat
Heat flux
Heat transfer coefficients
Hypotheses
Inequalities
Internal energy
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operators (mathematics)
Optimization
Original Paper
Simulation
Systems Theory
Theoretical
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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:0095-4616
1432-0606
DOI:10.1007/s00245-021-09800-9