Abstract
AbstractIn 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.
Funder
Horizon 2020
Beibu Gulf University
NSF of Guangxi
Ministerstwo Nauki i Szkolnictwa Wyższego
CONICETUA
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Control and Optimization
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