English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider an elliptic boundary value problem with unilateral constraintsand subdifferential boundary conditions. The problem describes the heattransfer in a domain $D\subset\R^d$ and its weak formulation is in the form ofa hemivariational inequality for the temperature field, denoted by $\cP$. Weassociate to Problem $\cP$ an optimal control problem, denoted by $\cQ$. Then,using appropriate Tykhonov triples, governed by a nonlinear operator $G$ and aconvex $\wK$, we provide results concerning the well-posedness of problems$\cP$ and $\cQ$. Our main results are Theorems 14 and 18, together with theircorollaries. Their proofs are based on arguments of compactness, lowersemicontinuity and pseudomonotonicity. Moreover, we consider three relevantperturbations of the heat transfer boundary valued problem which lead topenalty versions of Problem $\cP$, constructed with particular choices of $G$and $\wK$. We prove that Theorems 14 and 18 as well as their corollaries can beapplied in the study of these problems, in order to obtain various convergenceresults.

Tykhonov Well-posedness of a Heat Transfer Problem with Unilateral Constraints