Unconditional uniqueness and non-uniqueness for Hardy–Hénon parabolic equations

Unconditional uniqueness and non-uniqueness for Hardy–Hénon parabolic equations

We study the problems of uniqueness for Hardy–Hénon parabolic equations, which are semilinear heat equations with the singular potential (Hardy type) or the increasing potential (Hénon type) in the nonlinear term. To deal with the Hardy–Hénon type nonlinearities, we employ weighted Lorentz spaces as...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematische annalen 2024, Vol.390 (3), p.3765-3825
Hauptverfasser: Chikami, Noboru, Ikeda, Masahiro, Taniguchi, Koichi, Tayachi, Slim
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Nonlinearity
Solution space
Thermodynamics
Uniqueness
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 3825
container_issue 3
container_start_page 3765
container_title Mathematische annalen
container_volume 390
creator Chikami, Noboru
Ikeda, Masahiro
Taniguchi, Koichi
Tayachi, Slim
description We study the problems of uniqueness for Hardy–Hénon parabolic equations, which are semilinear heat equations with the singular potential (Hardy type) or the increasing potential (Hénon type) in the nonlinear term. To deal with the Hardy–Hénon type nonlinearities, we employ weighted Lorentz spaces as solution spaces. We prove unconditional uniqueness and non-uniqueness, and we establish uniqueness criterion for Hardy–Hénon parabolic equations in the weighted Lorentz spaces. The results extend the previous works on the Fujita equation and Hardy equations in Lebesgue spaces.
doi_str_mv 10.1007/s00208-024-02828-6
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3112100626</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3112100626</sourcerecordid><originalsourceid>FETCH-LOGICAL-c363t-8aea0eaca88a8e96682595bd4ed65e83aeb21420ef0d4238d3b07f28542bc4703</originalsourceid><addsrcrecordid>eNp9kMFKAzEQhoMoWKsv4GnBc3SSbLLpUYpaoSCIPYfZTVa21KRNuofefAefwufwTXwSU1fQk4dhYOb_f2Y-Qs4ZXDKA6ioBcNAUeJlLc03VARmxUnDKNFSHZJT3kkot2DE5SWkJAAJAjsjjwjfB227bBY-rovfdpnfepVSgt4UPnv4ZtSEWM4x29_n6Nvt4z9tijRHrsOqawm163KekU3LU4iq5s58-Jovbm6fpjM4f7u6n13PaCCW2VKNDcNig1qjdRCnN5UTWtnRWSacFupqzkoNrwZZcaCtqqFquZcnrpqxAjMnFkLuOIV-YtmYZ-pi_SEYwxjMXxVVW8UHVxJBSdK1Zx-4F484wMHt2ZmBnMjvzzc7sTWIwpSz2zy7-Rv_j-gLr_nQk</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3112100626</pqid></control><display><type>article</type><title>Unconditional uniqueness and non-uniqueness for Hardy–Hénon parabolic equations</title><source>SpringerLink Journals (MCLS)</source><creator>Chikami, Noboru ; Ikeda, Masahiro ; Taniguchi, Koichi ; Tayachi, Slim</creator><creatorcontrib>Chikami, Noboru ; Ikeda, Masahiro ; Taniguchi, Koichi ; Tayachi, Slim</creatorcontrib><description>We study the problems of uniqueness for Hardy–Hénon parabolic equations, which are semilinear heat equations with the singular potential (Hardy type) or the increasing potential (Hénon type) in the nonlinear term. To deal with the Hardy–Hénon type nonlinearities, we employ weighted Lorentz spaces as solution spaces. We prove unconditional uniqueness and non-uniqueness, and we establish uniqueness criterion for Hardy–Hénon parabolic equations in the weighted Lorentz spaces. The results extend the previous works on the Fujita equation and Hardy equations in Lebesgue spaces.</description><identifier>ISSN: 0025-5831</identifier><identifier>EISSN: 1432-1807</identifier><identifier>DOI: 10.1007/s00208-024-02828-6</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Mathematics ; Mathematics and Statistics ; Nonlinearity ; Solution space ; Thermodynamics ; Uniqueness</subject><ispartof>Mathematische annalen, 2024, Vol.390 (3), p.3765-3825</ispartof><rights>The Author(s) 2024</rights><rights>The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-8aea0eaca88a8e96682595bd4ed65e83aeb21420ef0d4238d3b07f28542bc4703</citedby><cites>FETCH-LOGICAL-c363t-8aea0eaca88a8e96682595bd4ed65e83aeb21420ef0d4238d3b07f28542bc4703</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00208-024-02828-6$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00208-024-02828-6$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Chikami, Noboru</creatorcontrib><creatorcontrib>Ikeda, Masahiro</creatorcontrib><creatorcontrib>Taniguchi, Koichi</creatorcontrib><creatorcontrib>Tayachi, Slim</creatorcontrib><title>Unconditional uniqueness and non-uniqueness for Hardy–Hénon parabolic equations</title><title>Mathematische annalen</title><addtitle>Math. Ann</addtitle><description>We study the problems of uniqueness for Hardy–Hénon parabolic equations, which are semilinear heat equations with the singular potential (Hardy type) or the increasing potential (Hénon type) in the nonlinear term. To deal with the Hardy–Hénon type nonlinearities, we employ weighted Lorentz spaces as solution spaces. We prove unconditional uniqueness and non-uniqueness, and we establish uniqueness criterion for Hardy–Hénon parabolic equations in the weighted Lorentz spaces. The results extend the previous works on the Fujita equation and Hardy equations in Lebesgue spaces.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinearity</subject><subject>Solution space</subject><subject>Thermodynamics</subject><subject>Uniqueness</subject><issn>0025-5831</issn><issn>1432-1807</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kMFKAzEQhoMoWKsv4GnBc3SSbLLpUYpaoSCIPYfZTVa21KRNuofefAefwufwTXwSU1fQk4dhYOb_f2Y-Qs4ZXDKA6ioBcNAUeJlLc03VARmxUnDKNFSHZJT3kkot2DE5SWkJAAJAjsjjwjfB227bBY-rovfdpnfepVSgt4UPnv4ZtSEWM4x29_n6Nvt4z9tijRHrsOqawm163KekU3LU4iq5s58-Jovbm6fpjM4f7u6n13PaCCW2VKNDcNig1qjdRCnN5UTWtnRWSacFupqzkoNrwZZcaCtqqFquZcnrpqxAjMnFkLuOIV-YtmYZ-pi_SEYwxjMXxVVW8UHVxJBSdK1Zx-4F484wMHt2ZmBnMjvzzc7sTWIwpSz2zy7-Rv_j-gLr_nQk</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>Chikami, Noboru</creator><creator>Ikeda, Masahiro</creator><creator>Taniguchi, Koichi</creator><creator>Tayachi, Slim</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2024</creationdate><title>Unconditional uniqueness and non-uniqueness for Hardy–Hénon parabolic equations</title><author>Chikami, Noboru ; Ikeda, Masahiro ; Taniguchi, Koichi ; Tayachi, Slim</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-8aea0eaca88a8e96682595bd4ed65e83aeb21420ef0d4238d3b07f28542bc4703</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinearity</topic><topic>Solution space</topic><topic>Thermodynamics</topic><topic>Uniqueness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chikami, Noboru</creatorcontrib><creatorcontrib>Ikeda, Masahiro</creatorcontrib><creatorcontrib>Taniguchi, Koichi</creatorcontrib><creatorcontrib>Tayachi, Slim</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Mathematische annalen</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chikami, Noboru</au><au>Ikeda, Masahiro</au><au>Taniguchi, Koichi</au><au>Tayachi, Slim</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Unconditional uniqueness and non-uniqueness for Hardy–Hénon parabolic equations</atitle><jtitle>Mathematische annalen</jtitle><stitle>Math. Ann</stitle><date>2024</date><risdate>2024</risdate><volume>390</volume><issue>3</issue><spage>3765</spage><epage>3825</epage><pages>3765-3825</pages><issn>0025-5831</issn><eissn>1432-1807</eissn><abstract>We study the problems of uniqueness for Hardy–Hénon parabolic equations, which are semilinear heat equations with the singular potential (Hardy type) or the increasing potential (Hénon type) in the nonlinear term. To deal with the Hardy–Hénon type nonlinearities, we employ weighted Lorentz spaces as solution spaces. We prove unconditional uniqueness and non-uniqueness, and we establish uniqueness criterion for Hardy–Hénon parabolic equations in the weighted Lorentz spaces. The results extend the previous works on the Fujita equation and Hardy equations in Lebesgue spaces.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00208-024-02828-6</doi><tpages>61</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0025-5831
ispartof Mathematische annalen, 2024, Vol.390 (3), p.3765-3825
issn 0025-5831
1432-1807
language eng
recordid cdi_proquest_journals_3112100626
source SpringerLink Journals (MCLS)
subjects Mathematics
Mathematics and Statistics
Nonlinearity
Solution space
Thermodynamics
Uniqueness
title Unconditional uniqueness and non-uniqueness for Hardy–Hénon parabolic equations
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-31T23%3A05%3A10IST&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=Unconditional%20uniqueness%20and%20non-uniqueness%20for%20Hardy%E2%80%93H%C3%A9non%20parabolic%20equations&rft.jtitle=Mathematische%20annalen&rft.au=Chikami,%20Noboru&rft.date=2024&rft.volume=390&rft.issue=3&rft.spage=3765&rft.epage=3825&rft.pages=3765-3825&rft.issn=0025-5831&rft.eissn=1432-1807&rft_id=info:doi/10.1007/s00208-024-02828-6&rft_dat=%3Cproquest_cross%3E3112100626%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3112100626&rft_id=info:pmid/&rfr_iscdi=true