On Attractors of Ginzburg–Landau Equations in Domain with Locally Periodic Microstructure: Subcritical, Critical, and Supercritical Cases

In the paper we consider a problem for complex Ginzburg–Landau equations in a medium with locally periodic small obstacles. It is assumed that the obstacle surface can have different conductivity coefficients. We prove that the trajectory attractors of this system converge in a certain weak topology...

Full description

Saved in:
Bibliographic Details
Published in:Doklady. Mathematics 2023-10, Vol.108 (2), p.346-351
Main Authors: Bekmaganbetov, K. A., Tolemys, A. A., Chepyzhov, V. V., Chechkin, G. A.
Format: Article
Language:English
Subjects:
Barriers
Landau-Ginzburg equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Topology
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c268t-4871ebdc58231a7083762a1aa6eb8f3cdf965eefff162daafa24795d722afca33
container_end_page 351
container_issue 2
container_start_page 346
container_title Doklady. Mathematics
container_volume 108
creator Bekmaganbetov, K. A.
Tolemys, A. A.
Chepyzhov, V. V.
Chechkin, G. A.
description In the paper we consider a problem for complex Ginzburg–Landau equations in a medium with locally periodic small obstacles. It is assumed that the obstacle surface can have different conductivity coefficients. We prove that the trajectory attractors of this system converge in a certain weak topology to the trajectory attractors of the homogenized Ginzburg–Landau equations with an additional potential (in the critical case), without an additional potential (in the subcritical case) in the medium without obstacles, or disappear (in the supercritical case).
doi_str_mv 10.1134/S1064562423701235
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2933033375</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2933033375</sourcerecordid><originalsourceid>FETCH-LOGICAL-c268t-4871ebdc58231a7083762a1aa6eb8f3cdf965eefff162daafa24795d722afca33</originalsourceid><addsrcrecordid>eNp1UMtKAzEUDaJgrX6Au4BbR_OYV92VsVZhpEJ1PdzJJDWlndQkg9SVe5f-oV9iSn0sxNU5cB6XexA6puSMUh6fTylJ4yRlMeMZoYwnO6hHE06jnKdsN_AgRxt9Hx04NyckThghPfQ2afHQewvCG-uwUXis25e6s7OP1_cS2gY6PHrqwGvTOqxbfGmWEOBZ-0dcGgGLxRrfSatNowW-1cIa520nfGflBZ52tbDa62A7xcUPC7VBWkn7LeICnHSHaE_BwsmjL-yjh6vRfXEdlZPxTTEsI8HS3EdxnlFZNyLJGaeQkZxnKQMKkMo6V1w0apAmUiqlaMoaAAUszgZJkzEGSgDnfXSy7V1Z89RJ56u56WwbTlZswDnhnGdJcNGta_OSs1JVK6uXYNcVJdVm8-rP5iHDthkXvO1M2t_m_0OfmgmGgg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2933033375</pqid></control><display><type>article</type><title>On Attractors of Ginzburg–Landau Equations in Domain with Locally Periodic Microstructure: Subcritical, Critical, and Supercritical Cases</title><source>Springer Nature</source><creator>Bekmaganbetov, K. A. ; Tolemys, A. A. ; Chepyzhov, V. V. ; Chechkin, G. A.</creator><creatorcontrib>Bekmaganbetov, K. A. ; Tolemys, A. A. ; Chepyzhov, V. V. ; Chechkin, G. A.</creatorcontrib><description>In the paper we consider a problem for complex Ginzburg–Landau equations in a medium with locally periodic small obstacles. It is assumed that the obstacle surface can have different conductivity coefficients. We prove that the trajectory attractors of this system converge in a certain weak topology to the trajectory attractors of the homogenized Ginzburg–Landau equations with an additional potential (in the critical case), without an additional potential (in the subcritical case) in the medium without obstacles, or disappear (in the supercritical case).</description><identifier>ISSN: 1064-5624</identifier><identifier>EISSN: 1531-8362</identifier><identifier>DOI: 10.1134/S1064562423701235</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Barriers ; Landau-Ginzburg equations ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Topology</subject><ispartof>Doklady. Mathematics, 2023-10, Vol.108 (2), p.346-351</ispartof><rights>Pleiades Publishing, Ltd. 2023. ISSN 1064-5624, Doklady Mathematics, 2023, Vol. 108, No. 2, pp. 346–351. © Pleiades Publishing, Ltd., 2023. ISSN 1064-5624, Doklady Mathematics, 2023. © Pleiades Publishing, Ltd., 2023. Russian Text © The Author(s), 2023, published in Doklady Rossiiskoi Akademii Nauk. Matematika, Informatika, Protsessy Upravleniya, 2023, Vol. 513, pp. 9–14.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-4871ebdc58231a7083762a1aa6eb8f3cdf965eefff162daafa24795d722afca33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Bekmaganbetov, K. A.</creatorcontrib><creatorcontrib>Tolemys, A. A.</creatorcontrib><creatorcontrib>Chepyzhov, V. V.</creatorcontrib><creatorcontrib>Chechkin, G. A.</creatorcontrib><title>On Attractors of Ginzburg–Landau Equations in Domain with Locally Periodic Microstructure: Subcritical, Critical, and Supercritical Cases</title><title>Doklady. Mathematics</title><addtitle>Dokl. Math</addtitle><description>In the paper we consider a problem for complex Ginzburg–Landau equations in a medium with locally periodic small obstacles. It is assumed that the obstacle surface can have different conductivity coefficients. We prove that the trajectory attractors of this system converge in a certain weak topology to the trajectory attractors of the homogenized Ginzburg–Landau equations with an additional potential (in the critical case), without an additional potential (in the subcritical case) in the medium without obstacles, or disappear (in the supercritical case).</description><subject>Barriers</subject><subject>Landau-Ginzburg equations</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Topology</subject><issn>1064-5624</issn><issn>1531-8362</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1UMtKAzEUDaJgrX6Au4BbR_OYV92VsVZhpEJ1PdzJJDWlndQkg9SVe5f-oV9iSn0sxNU5cB6XexA6puSMUh6fTylJ4yRlMeMZoYwnO6hHE06jnKdsN_AgRxt9Hx04NyckThghPfQ2afHQewvCG-uwUXis25e6s7OP1_cS2gY6PHrqwGvTOqxbfGmWEOBZ-0dcGgGLxRrfSatNowW-1cIa520nfGflBZ52tbDa62A7xcUPC7VBWkn7LeICnHSHaE_BwsmjL-yjh6vRfXEdlZPxTTEsI8HS3EdxnlFZNyLJGaeQkZxnKQMKkMo6V1w0apAmUiqlaMoaAAUszgZJkzEGSgDnfXSy7V1Z89RJ56u56WwbTlZswDnhnGdJcNGta_OSs1JVK6uXYNcVJdVm8-rP5iHDthkXvO1M2t_m_0OfmgmGgg</recordid><startdate>20231001</startdate><enddate>20231001</enddate><creator>Bekmaganbetov, K. A.</creator><creator>Tolemys, A. A.</creator><creator>Chepyzhov, V. V.</creator><creator>Chechkin, G. A.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20231001</creationdate><title>On Attractors of Ginzburg–Landau Equations in Domain with Locally Periodic Microstructure: Subcritical, Critical, and Supercritical Cases</title><author>Bekmaganbetov, K. A. ; Tolemys, A. A. ; Chepyzhov, V. V. ; Chechkin, G. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-4871ebdc58231a7083762a1aa6eb8f3cdf965eefff162daafa24795d722afca33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Barriers</topic><topic>Landau-Ginzburg equations</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bekmaganbetov, K. A.</creatorcontrib><creatorcontrib>Tolemys, A. A.</creatorcontrib><creatorcontrib>Chepyzhov, V. V.</creatorcontrib><creatorcontrib>Chechkin, G. A.</creatorcontrib><collection>CrossRef</collection><jtitle>Doklady. Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bekmaganbetov, K. A.</au><au>Tolemys, A. A.</au><au>Chepyzhov, V. V.</au><au>Chechkin, G. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Attractors of Ginzburg–Landau Equations in Domain with Locally Periodic Microstructure: Subcritical, Critical, and Supercritical Cases</atitle><jtitle>Doklady. Mathematics</jtitle><stitle>Dokl. Math</stitle><date>2023-10-01</date><risdate>2023</risdate><volume>108</volume><issue>2</issue><spage>346</spage><epage>351</epage><pages>346-351</pages><issn>1064-5624</issn><eissn>1531-8362</eissn><abstract>In the paper we consider a problem for complex Ginzburg–Landau equations in a medium with locally periodic small obstacles. It is assumed that the obstacle surface can have different conductivity coefficients. We prove that the trajectory attractors of this system converge in a certain weak topology to the trajectory attractors of the homogenized Ginzburg–Landau equations with an additional potential (in the critical case), without an additional potential (in the subcritical case) in the medium without obstacles, or disappear (in the supercritical case).</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1064562423701235</doi><tpages>6</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1064-5624
ispartof Doklady. Mathematics, 2023-10, Vol.108 (2), p.346-351
issn 1064-5624
1531-8362
language eng
recordid cdi_proquest_journals_2933033375
source Springer Nature
subjects Barriers
Landau-Ginzburg equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Topology
title On Attractors of Ginzburg–Landau Equations in Domain with Locally Periodic Microstructure: Subcritical, Critical, and Supercritical Cases
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-01T19%3A39%3A54IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20Attractors%20of%20Ginzburg%E2%80%93Landau%20Equations%20in%20Domain%20with%20Locally%20Periodic%20Microstructure:%20Subcritical,%20Critical,%20and%20Supercritical%20Cases&rft.jtitle=Doklady.%20Mathematics&rft.au=Bekmaganbetov,%20K.%20A.&rft.date=2023-10-01&rft.volume=108&rft.issue=2&rft.spage=346&rft.epage=351&rft.pages=346-351&rft.issn=1064-5624&rft.eissn=1531-8362&rft_id=info:doi/10.1134/S1064562423701235&rft_dat=%3Cproquest_cross%3E2933033375%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c268t-4871ebdc58231a7083762a1aa6eb8f3cdf965eefff162daafa24795d722afca33%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2933033375&rft_id=info:pmid/&rfr_iscdi=true