Properties of a quasi-uniformly monotone operator and its application to the electromagnetic p-curl systems
In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of nonlinear operator equation Au = b . We prove that if A is a quasi-uniformly monotone and hemi-continuous operator, then A −1 is strictly monotone, bound...
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| Veröffentlicht in: | Applications of mathematics (Prague) 2022-08, Vol.67 (4), p.431-444 |
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| creator | Song, Chang-Ho Ri, Yong-Gon Sin, Cholmin |
| description | In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of nonlinear operator equation
Au
=
b
. We prove that if
A
is a quasi-uniformly monotone and hemi-continuous operator, then
A
−1
is strictly monotone, bounded and continuous, and thus the Galerkin approximations converge. Also we show an application of a quasi-uniformly monotone and hemi-continuous operator to the proof of the well-posedness and convergence of Galerkin approximations to the solution of steady-state electromagnetic
p
-curl systems. |
| doi_str_mv | 10.21136/AM.2021.0365-20 |
| format | Article |
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Au
=
b
. We prove that if
A
is a quasi-uniformly monotone and hemi-continuous operator, then
A
−1
is strictly monotone, bounded and continuous, and thus the Galerkin approximations converge. Also we show an application of a quasi-uniformly monotone and hemi-continuous operator to the proof of the well-posedness and convergence of Galerkin approximations to the solution of steady-state electromagnetic
p
-curl systems.</description><identifier>ISSN: 0862-7940</identifier><identifier>EISSN: 1572-9109</identifier><identifier>DOI: 10.21136/AM.2021.0365-20</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Applications of Mathematics ; Classical and Continuum Physics ; Convergence ; Galerkin method ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Optimization ; Theoretical</subject><ispartof>Applications of mathematics (Prague), 2022-08, Vol.67 (4), p.431-444</ispartof><rights>Institute of Mathematics, Czech Academy of Sciences 2021</rights><rights>Institute of Mathematics, Czech Academy of Sciences 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p225t-acefaf59504da5bcf5c812657401f170b2d3aeea8504ef5a00d0fc39be7efa0c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.21136/AM.2021.0365-20$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.21136/AM.2021.0365-20$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Song, Chang-Ho</creatorcontrib><creatorcontrib>Ri, Yong-Gon</creatorcontrib><creatorcontrib>Sin, Cholmin</creatorcontrib><title>Properties of a quasi-uniformly monotone operator and its application to the electromagnetic p-curl systems</title><title>Applications of mathematics (Prague)</title><addtitle>Appl Math</addtitle><description>In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of nonlinear operator equation
Au
=
b
. We prove that if
A
is a quasi-uniformly monotone and hemi-continuous operator, then
A
−1
is strictly monotone, bounded and continuous, and thus the Galerkin approximations converge. Also we show an application of a quasi-uniformly monotone and hemi-continuous operator to the proof of the well-posedness and convergence of Galerkin approximations to the solution of steady-state electromagnetic
p
-curl systems.</description><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Classical and Continuum Physics</subject><subject>Convergence</subject><subject>Galerkin method</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Optimization</subject><subject>Theoretical</subject><issn>0862-7940</issn><issn>1572-9109</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNpFkD1PwzAURS0EEqWwM1pidnl26jgZq4ovqRUMMEeu81xcUju1nYF_T0qRmN4dzr1POoTccpgJzovyfrGeCRB8BkUpmYAzMuFSCVZzqM_JBKpSMFXP4ZJcpbQDgLqsqgn5eouhx5gdJhos1fQw6OTY4J0Ncd99033wIQeP9IjpHCLVvqUuJ6r7vnNGZxc8zYHmT6TYockx7PXWY3aG9swMsaPpO2Xcp2tyYXWX8ObvTsnH48P78pmtXp9elosV64WQmWmDVltZS5i3Wm6MlabiopRqDtxyBRvRFhpRVyOAVmqAFqwp6g2qsQimmJK7024fw2HAlJtdGKIfXzairECoUnE1UvxEpT46v8X4T3Fofp02i3VzdNocnY6p-AHyi2zH</recordid><startdate>20220801</startdate><enddate>20220801</enddate><creator>Song, Chang-Ho</creator><creator>Ri, Yong-Gon</creator><creator>Sin, Cholmin</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20220801</creationdate><title>Properties of a quasi-uniformly monotone operator and its application to the electromagnetic p-curl systems</title><author>Song, Chang-Ho ; Ri, Yong-Gon ; Sin, Cholmin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p225t-acefaf59504da5bcf5c812657401f170b2d3aeea8504ef5a00d0fc39be7efa0c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Classical and Continuum Physics</topic><topic>Convergence</topic><topic>Galerkin method</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Optimization</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Song, Chang-Ho</creatorcontrib><creatorcontrib>Ri, Yong-Gon</creatorcontrib><creatorcontrib>Sin, Cholmin</creatorcontrib><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Applications of mathematics (Prague)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Song, Chang-Ho</au><au>Ri, Yong-Gon</au><au>Sin, Cholmin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Properties of a quasi-uniformly monotone operator and its application to the electromagnetic p-curl systems</atitle><jtitle>Applications of mathematics (Prague)</jtitle><stitle>Appl Math</stitle><date>2022-08-01</date><risdate>2022</risdate><volume>67</volume><issue>4</issue><spage>431</spage><epage>444</epage><pages>431-444</pages><issn>0862-7940</issn><eissn>1572-9109</eissn><abstract>In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of nonlinear operator equation
Au
=
b
. We prove that if
A
is a quasi-uniformly monotone and hemi-continuous operator, then
A
−1
is strictly monotone, bounded and continuous, and thus the Galerkin approximations converge. Also we show an application of a quasi-uniformly monotone and hemi-continuous operator to the proof of the well-posedness and convergence of Galerkin approximations to the solution of steady-state electromagnetic
p
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| ispartof | Applications of mathematics (Prague), 2022-08, Vol.67 (4), p.431-444 |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Springer Nature - Complete Springer Journals |
| subjects | Analysis Applications of Mathematics Classical and Continuum Physics Convergence Galerkin method Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Optimization Theoretical |
| title | Properties of a quasi-uniformly monotone operator and its application to the electromagnetic p-curl systems |
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