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...

Full description

Saved in:
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)
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Gariboldi, Claudia M
Migórski, Stanisław
Ochal, Anna
Tarzia, Domingo A
description 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.
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2539743439</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2539743439</sourcerecordid><originalsourceid>FETCH-proquest_journals_25397434393</originalsourceid><addsrcrecordid>eNqNi00KwjAQRoMgWLR3GHCrUJPWn7UoHsC9DHGqU9KkZtLi8a3gAVw9Pt73JirTxmzW-1LrmcpFmqIo9Hanq8pkyp7eLIm8pRXY0HYYWYJfAfr7uP1A8fGVEEl6lwTqEAHBOhSBUAM5x11iC09qeRhjTBw8OmBPrx4dJyZZqGmNTij_ca6W59P1eFl3Mbx6knRrQh_HSm66ModdaUpzMP-9PjSdRuw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2539743439</pqid></control><display><type>article</type><title>Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities</title><source>Publicly Available Content Database</source><creator>Gariboldi, Claudia M ; Migórski, Stanisław ; Ochal, Anna ; Tarzia, Domingo A</creator><creatorcontrib>Gariboldi, Claudia M ; Migórski, Stanisław ; Ochal, Anna ; Tarzia, Domingo A</creatorcontrib><description>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.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Asymptotic properties ; Boundary conditions ; Conduction heating ; Conductive heat transfer ; Heat flux ; Heat transfer coefficients ; Inequalities ; Internal energy ; Operators (mathematics)</subject><ispartof>arXiv.org, 2021-06</ispartof><rights>2021. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2539743439?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>780,784,25753,37012,44590</link.rule.ids></links><search><creatorcontrib>Gariboldi, Claudia M</creatorcontrib><creatorcontrib>Migórski, Stanisław</creatorcontrib><creatorcontrib>Ochal, Anna</creatorcontrib><creatorcontrib>Tarzia, Domingo A</creatorcontrib><title>Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities</title><title>arXiv.org</title><description>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.</description><subject>Asymptotic properties</subject><subject>Boundary conditions</subject><subject>Conduction heating</subject><subject>Conductive heat transfer</subject><subject>Heat flux</subject><subject>Heat transfer coefficients</subject><subject>Inequalities</subject><subject>Internal energy</subject><subject>Operators (mathematics)</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqNi00KwjAQRoMgWLR3GHCrUJPWn7UoHsC9DHGqU9KkZtLi8a3gAVw9Pt73JirTxmzW-1LrmcpFmqIo9Hanq8pkyp7eLIm8pRXY0HYYWYJfAfr7uP1A8fGVEEl6lwTqEAHBOhSBUAM5x11iC09qeRhjTBw8OmBPrx4dJyZZqGmNTij_ca6W59P1eFl3Mbx6knRrQh_HSm66ModdaUpzMP-9PjSdRuw</recordid><startdate>20210608</startdate><enddate>20210608</enddate><creator>Gariboldi, Claudia M</creator><creator>Migórski, Stanisław</creator><creator>Ochal, Anna</creator><creator>Tarzia, Domingo A</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20210608</creationdate><title>Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities</title><author>Gariboldi, Claudia M ; Migórski, Stanisław ; Ochal, Anna ; Tarzia, Domingo A</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_25397434393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Asymptotic properties</topic><topic>Boundary conditions</topic><topic>Conduction heating</topic><topic>Conductive heat transfer</topic><topic>Heat flux</topic><topic>Heat transfer coefficients</topic><topic>Inequalities</topic><topic>Internal energy</topic><topic>Operators (mathematics)</topic><toplevel>online_resources</toplevel><creatorcontrib>Gariboldi, Claudia M</creatorcontrib><creatorcontrib>Migórski, Stanisław</creatorcontrib><creatorcontrib>Ochal, Anna</creatorcontrib><creatorcontrib>Tarzia, Domingo A</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gariboldi, Claudia M</au><au>Migórski, Stanisław</au><au>Ochal, Anna</au><au>Tarzia, Domingo A</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities</atitle><jtitle>arXiv.org</jtitle><date>2021-06-08</date><risdate>2021</risdate><eissn>2331-8422</eissn><abstract>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.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2021-06
issn 2331-8422
language eng
recordid cdi_proquest_journals_2539743439
source Publicly Available Content Database
subjects Asymptotic properties
Boundary conditions
Conduction heating
Conductive heat transfer
Heat flux
Heat transfer coefficients
Inequalities
Internal energy
Operators (mathematics)
title Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T12%3A19%3A00IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Existence,%20comparison,%20and%20convergence%20results%20for%20a%20class%20of%20elliptic%20hemivariational%20inequalities&rft.jtitle=arXiv.org&rft.au=Gariboldi,%20Claudia%20M&rft.date=2021-06-08&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2539743439%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_25397434393%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2539743439&rft_id=info:pmid/&rfr_iscdi=true